MASSIVE PARALLEL DECODING OF LOW-DENSITY PARITY-CHECK CODES USING GRAPHIC CARDS

The belief propagation decoder for LDPS codes is ported to CUDATM and optimized for a high amount of parallel computation. The resulting implementation shall be compared with a non-parallel version on state-of-the-art PCs.Monzó Solves, E. (2010). MASSIVE PARALLEL DECODING OF LOW-DENSITY PARITY-CHECK CODES USING GRAPHIC CARDS. Universitat Politècnica de València. http://hdl.handle.net/10251/1373

Possibly your rooms may have defects. Like men, few are perfect: comedores y género en el ámbito anglosajón

El interior doméstico del siglo XIX se adaptaba a las necesidades privadas y públicas de la clase burguesa. Las diversas estancias, su distribución y su ornamentación se sometían a los dictados de la moda, pero también a unas exigencias familiares y sociales cuidadosamente codificadas. En esta época, uno de los espacios más destacados dentro del hogar era el comedor. Este constituía una estancia de representación destacada, donde la familia podía exhibir su posición dentro de la sociedad y, asimismo, era un lugar en el que sus miembros podían reunirse en intimidad. Los manuales normativos y los libros sobre decoración otorgaron a esta habitación un carácter masculino y ello condicionó su diseño. Sin embargo, aunque el género está presente también en la vivienda del Ochocientos, los límites que se establecen entre lo femenino y lo masculino no siempre están tan claros. Ahí el interés, el valor y quizás también el misterio de un espacio creado para el devenir de lo cotidiano.Nineteenth Century domestic interiors were adapted to private and public needs of the bourgeois class. The different rooms, their distribution and ornamentation were subjected to the dictates of fashion, but also to the family and social expectations of that time. One of the most outstanding spaces within the home was the dining room. This was an area where the family could demonstrate their status in society and a place where its members could meet in privacy. The etiquette manuals and books on decorating gave this room a male character and this determined its design. However, while gender is also present in the housing of the 19th Century, the boundaries established between the feminine and masculine are not always so clear. Hence, the interest, value and perhaps also the mystery of a space created for the development of the everyda

Every separable complex Fréchet space with a continuous norm is isomorphic to a space of holomorphic functions

[EN] Extending a result of Mashreghi and Ransford, we prove that every complex separable infinite-dimensional Frechet space with a continuous norm is isomorphic to a space continuously included in a space of holomorphic functions on the unit disc or the complex plane, which contains the polynomials as a dense subspace. As a consequence, we deduce the existence of nuclear Frechet spaces of holomorphic functions without the bounded approximationThiis research was partially supported by the projects MTMMTM2016-76647-P and GV Prometeo/2017/102Bonet Solves, JA. (2021). Every separable complex Fréchet space with a continuous norm is isomorphic to a space of holomorphic functions. Canadian Mathematical Bulletin. 64(1):8-12. https://doi.org/10.4153/S000843952000017XS81264

The spectrum of Volterra operators on Korenblum type spaces of analytic functions

[EN] The continuity, compactness and the spectrum of the Volterra integral operator V-g with symbol an analytic function g, when acting on the classical Korenblum space and other related weighted Frechet or (LB) spaces of analytic functions on the open unit disc, are investigated.This research was partially supported by the Projects MTM2016-76647-P and GV Prometeo/2017/102.Bonet Solves, JA. (2019). The spectrum of Volterra operators on Korenblum type spaces of analytic functions. Integral Equations and Operator Theory. 91(5):1-16. https://doi.org/10.1007/s00020-019-2547-x116915Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in growth Banach spaces of analytic functions. Integral Equ. Oper. Theory 86, 97–112 (2016)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on Korenblum type spaces of analytic functions. Collect. Math. 69, 263–281 (2018)Aleman, A., Constantin, O.: Spectra of integration operators on weighted Bergman spaces. J. Anal. Math. 109, 199–231 (2009)Aleman, A., Peláez, J.A.: Spectra of integration operators and weighted square functions. Indiana Univ. Math. J. 61, 1–19 (2012)Aleman, A., Persson, A.-M.: Resolvent estimates and decomposable extensions of generalized Cesàro operators. J. Funct. Anal. 258, 67–98 (2010)Aleman, A., Siskakis, A.G.: An integral operator on $$H^p$$. Complex Var. Theory Appl. 28, 149–158 (1995)Aleman, A., Siskakis, A.G.: Integration operators on Bergman spaces. Indiana Univ. Math. J. 46, 337–356 (1997)Basallote, M., Contreras, M.D., Hernández-Mancera, C., Martín, M.J., Paúl, P.J.: Volterra operators and semigroups in weighted Banach spaces of analytic functions. Collect. Math. 65, 233–249 (2014)Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Stud. Math. 127, 137–168 (1998)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Austral. Math. Soc. Ser. A 54(1), 70–79 (1993)Blasco, O., Girela, D., Márquez, M.A.: Mean growth of the derivative of analytic functions, bounded mean oscillation and normal functions. Indiana Univ. Math. J. 47, 893–912 (1998)Bonet, J.: The spectrum of Volterra operators on weighted spaces of entire functions. Q. J. Math. 66, 799–807 (2015)Constantin, O.: A Volterra-type integration operator on Fock spaces. Proc. Am. Math. Soc. 140, 4247–4257 (2012)Constantin, O., Persson, A.-M.: The spectrum of Volterra-type integration operators on generalized Fock spaces. Bull. London Math. Soc. 47, 958–963 (2015)Contreras, M., Hernández-Díaz, A.G.: Weighted composition operators in weighted Banach spacs of analytic functions. J. Austral. Math. Soc. (Ser. A) 69, 41–60 (2000)Duren, P.: Theory of $$H^p$$ Spaces. Academic Press, New York (1970)Girela, D., González, C., Peláez, J.A.: Multiplication and division by inner functions in the space of Bloch functions. Proc. Am. Math. Soc. 134, 1309–1314 (2006)Harutyunyan, A., Lusky, W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Stud. Math. 184, 233–247 (2008)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Grad. Texts in Math. 199, Springer, New York (2000)Hu, Z.: Extended Cesàro operators on mixed-norm spaces. Proc. Am. Math. Soc. 131, 2171–2179 (2003)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187–219 (1975)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomophic functions. Stud. Math. 75, 19–45 (2006)Malman, B.: Spectra of generalized Cesáro operators acting on growth spaces. Integr. Equ. Oper. Theory 90, 26 (2018)Meise, R., Vogt, D.: Introduction to Functional Analysis, Vol 2 of Oxford Graduate Texts in Mathematics. The Clarendon Press, New York (1997)Persson, A.-M.: On the spectrum of the Cesàro operator on spaces of analytic functions. J. Math. Anal. Appl. 340, 1180–1203 (2008)Pommerenke, C.: Schlichte Funktionen un analytische Functionen von beschrn̈kter mittlerer Oszilation. Comment. Math. Helv. 52, 591–602 (1977)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971)Siskakis, A.: Volterra operators on spaces of analytic functions–a survey. In: Proceedings of the First Advanced Course in Operator Theory and Complex Analysis, Univ. Sevilla Serc. Publ., Seville, 2006, pp. 51–68 (2006)Stević, S.: Boundedness and compactness of an integral operator on a weighted space on the polydisc. Indian J. Pure Appl. Math. 37, 343–355 (2006)Vasilescu, F.H.: Analytic functional calculus and spectral decompositions. Translated from the Romanian. Mathematics and its Applications (East European Series), 1. D. Reidel Publishing Co., Dordrecht (1982)Zhu, K.: Operator Theory on Function Spaces, Math. Surveys and Monographs Vo. 138. Amer. Math. Soc. (2007

Weighted Banach spaces of analytic functions with sup-norms and operators between them: a survey

[EN] In this survey we report about recent work on weighted Banach spaces of analytic functions on the unit disc and on the whole complex plane defined with sup-norms and operators between them. Results about the solid hull and core of these spaces and distance formulas are reviewed. Differentiation and integration operators, Cesaro and Volterra operators, weighted composition and superposition operators and Toeplitz operators on these spaces are analyzed. Boundedness, compactness, the spectrum, hypercyclicity and (uniform) mean ergodicity of these operators are considered.This research was partially supported by the project MCIN PID2020-119457GB-I00/AEI/10.13039/501100011033. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.Bonet Solves, JA. (2022). Weighted Banach spaces of analytic functions with sup-norms and operators between them: a survey. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 116(4):1-40. https://doi.org/10.1007/s13398-022-01323-41401164Abakumov, E., Doubtsov, E.: Reverse estimates in growth spaces. Math. Z. 271(1–2), 399–413 (2012)Abakumov, E., Doubtsov, E.: Moduli of holomorphic functions and logarithmically convex radial weights. Bull. Lond. Math. Soc. 47(3), 519–532 (2015)Abakumov, E., Doubtsov, E.: Approximation by proper holomorphic maps and tropical power series. Constr. Approx. 47(2), 321–338 (2018)Abakumov, E., Doubtsov, E.: Volterra type operators on growth Fock spaces. Arch. Math. (Basel) 108(4), 383–393 (2017)Abakumov, E., Doubtsov, E.: Univalent symbols of Volterra operators on growth spaces. Anal. Math. Phys. 9(3), 911–917 (2019)Abanin, A.V., Tien, P.T.: Differentiation and integration operators on weighted Banach spaces of holomorphic functions. Math. Nachr. 290(8–9), 1144–1162 (2017)Abanin, A.V., Tien, P.T.: Invariant subspaces for classical operators on weighted spaces of holomorphic functions. Integral Equ. Oper. Theory 89(3), 409–438 (2017)Abanin, A.V., Tien, P.T.: Compactness of classical operators on weighted Banach spaces of holomorphic functions. Collect. Math. 69(1), 1–15 (2018)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in growth Banach spaces of analytic functions. Integral Equ. Oper. Theory 86(1), 97–112 (2016)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on Korenblum type spaces of analytic functions. Collect. Math. 69(2), 263–281 (2018)Aleman, A., Constantin, O.: Spectra of integration operators on weighted Bergman spaces. J. Anal. Math. 109, 199–231 (2009)Aleman, A., Montes-Rodríguez, A., Sarafoleanu, A.: The eigenfunctions of the Hilbert matrix. Constr. Approx. 36(3), 353–374 (2012)Aleman, A., Peláez, J.A.: Spectra of integration operators and weighted square functions. Indiana Univ. Math. J. 61, 1–19 (2012)Aleman, A., Persson, A.-M.: Resolvent estimates and decomposable extensions of generalized Cesàro operators. J. Funct. Anal. 258, 67–98 (2010)Aleman, A., Siskakis, A.G.: An integral operator on $$H^p$$. Complex Var. Theory Appl. 28, 149–158 (1995)Aleman, A., Siskakis, A.G.: Integration operators on Bergman spaces. Indiana Univ. Math. J. 46, 337–356 (1997)Anderson, A., Jovovic, M., Smith, W.: Some integral operators acting on $$H^\infty$$. Integral Equ. Oper. Theory 80, 275–291 (2014)Anderson, J.M., Shields, A.L.: Coefficient multipliers of Bloch functions. Trans. Am. Math. Soc. 224, 255–265 (1976)Arcozzi, N., Björn, A.: Dominating sets for analytic and harmonic functions and completeness of weighted Bergman spaces. Math. Proc. R. Ir. Acad. 102A, 175–192 (2002)Arendt, W., Célariès, B., Chalendar, I.: In Koenigs’ footsteps: diagonalization of composition operators. J. Funct. Anal. 278(2), 108313 (2002)Arendt, W., Chalendar, I., Kumar, M., Srivastava, S.: Asymptotic behaviour of the powers of composition operators on Banach spaces of holomorphic functions. Indiana Univ. Math. J. 67(4), 1571–1595 (2018)Arendt, W., Chalendar, I., Kumar, M., Srivastava, S.: Powers of composition operators: asymptotic behaviour on Bergman, Dirichlet and Bloch spaces. J. Aust. Math. Soc. 108(3), 289–320 (2020)Aron, R., Lindström, M.: Spectra of weighted composition operators on weighted Banach spaces of analytic functions. Isr. J. Math. 141, 263–276 (2004)Atzmon, A., Brive, B.: Surjectivity and invariant subspaces of differential operators on weighted Bergman spaces of entire functions, Bergman spaces and related topics in complex analysis, pp. 27–39, Contemp. Math., vol. 404. Amer. Math. Soc., Providence (2006)Basallote, M., Contreras, M.D., Hernández-Mancera, C., Martín, M.J., Paúl, P.J.: Volterra operators and semigroups in weighted Banach spaces of analytic functions. Collect. Math. 65(2), 233–249 (2014)Bayart, F., Matheron, É.: Dynamics of Linear Operators. Cambridge University Press, Cambridge (2009)Beltrán-Meneu, M.J.: Dynamics of differentiation and integration operators on weighted spaces of entire functions. Studia Math. 221(1), 35–60 (2014)Beltrán-Meneu, M.J.: Dynamics of weighted composition operators on weighted Banach spaces of entire functions. J. Math. Anal. Appl. 492(1), 124422 (2020)Beltrán-Meneu, M.J., Jordá, E.: Dynamics of weighted composition operators on spaces of entire functions of exponential and infraexponential type. Mediterr. J. Math. 18(5), Paper No. 212 (2021)Beltrán-Meneu, M.J., Bonet, J., Fernández, C.: Classical operators on weighted Banach spaces of entire functions. Proc. Am. Math. Soc. 141(12), 4293–4303 (2013)Beltrán-Meneu, M.J., Bonet, J., Fernández, C.: Classical operators on the Hörmander algebras. Discrete Contin. Dyn. Syst. 35(2), 637–652 (2015)Beltrán-Meneu, M.J., Gómez-Collado, M.C., Jordá, E., Jornet, D.: Mean ergodic composition operators on Banach spaces of holomorphic functions. J. Funct. Anal. 270(12), 4369–4385 (2016)Beltrán-Meneu, M.J., Gómez-Collado, M.C., Jordá, E., Jornet, D.: Mean ergodicity of weighted composition operators on spaces of holomorphic functions. J. Math. Anal. Appl. 444(2), 1640–1651 (2016)Bennet, G., Stegenga, D.A., Timoney, R.M.: Coefficients of Bloch and Lipschitz functions. Ill. J. Math. 25, 520–531 (1981)Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on bounded domains. Mich. Math. J. 40, 271–297 (1993)Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Studia Math. 127, 137–168 (1998)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Aust. Math. Soc. 54, 70–79 (1993)Blasco, O.: Operators on Fock-type and weighted spaces of entire functions. Funct. Approx. Comment. Math. 59(2), 175–189 (2018)Blasco, O.: Boundedness of Volterra operators on spaces of entire functions. Ann. Acad. Sci. Fenn. Math. 43(1), 89–107 (2018)Bonet, J.: Weighted spaces of holomorphic functions and operators between them. Seminar of Mathematical Analysis (Malaga/Seville, 2002/2003), pp. 117–138, Colecc. Abierta, vol. 64. Univ. Sevilla Secr. Publ., Seville (2003)Bonet, J.: A note about the spectrum of composition operators induced by a rotation. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114(2), 63 (2020)Bonet, J.: The spectrum of Volterra operators on Korenblum type spaces of analytic functions. Integral Equ. Oper. Theory 91(5), Paper No. 46 (2019)Bonet, J.: The spectrum of Volterra operators on weighted spaces of entire functions. Q. J. Math. 66(3), 799–807 (2015)Bonet, J.: Dynamics of the differentiation operator on weighted spaces of entire functions. Math. Z. 261(3), 649–657 (2009)Bonet, J.: Hausdorff operators on weighted Banach spaces of type $$H^\infty$$. Complex Anal. Oper. Theory 16(1), Paper No. 12 (2022)Bonet, J., Bonilla, A.: Chaos of the differentiation operator on weighted Banach spaces of entire functions. Complex Anal. Oper. Theory 7, 33–42 (2013)Bonet, J., Domański, P.: A note on mean ergodic composition operators on spaces of holomorphic functions. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 105(2), 389–396 (2011)Bonet, J., Domański, P.: Power bounded composition operators on spaces of analytic functions. Collect. Math. 62(1), 69–83 (2011)Bonet, J., Domański, P., Lindström, M.: Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions. Can. Math. Bull. 42, 139–148 (1999)Bonet, J., Domański, P., Lindström, M.: Pointwise multiplication operators on weighted Banach spaces of analytic functions. Studia Math. 137, 177–194 (1999)Bonet, J., Domański, P., Lindström, M.: Weakly compact composition operators on analytic vector-valued function spaces. Ann. Acad. Sci. Fenn. 26, 233–248 (2001)Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Aust. Math. Soc. 64, 101–118 (1998)Bonet, J., Galbis, A.: Invariant subspaces of the integration operators on Hörmander algebras and Korenblum type spaces. Integral Equ. Oper. Theory 92(4), Paper No. 34 (2020)Bonet, J., Galindo, P., Lindström, M.: Spectra and essential spectral radii of composition operators on weighted Banach spaces of analytic functions. J. Math. Anal. Appl. 340(2), 884–891 (2008)Bonet, J., Gómez-Collado, M.C., Jordá, E., Jornet, D.: Nuclear weighted composition operators on weighted Banach spaces of analytic functions. Proc. Am. Math. Soc. 149(1), 311–321 (2021)Bonet, J., Lindström, M., Wolf, E.: Isometric weighted composition operators on weighted Banach spaces of type $$H^{\infty }$$. Proc. Am. Math. Soc. 136(12), 4267–4273 (2008)Bonet, J., Lusky, W., Taskinen, J.: Distance formulas on weighted Banach spaces of analytic functions. Complex Anal. Oper. Theory 13(3), 893–900 (2019)Bonet, J., Lusky, W., Taskinen, J.: Solid hulls and cores of weighted $$H^{\infty }$$-spaces. Rev. Mat. Complut. 31(3), 781–804 (2019)Bonet, J., Lusky, W., Taskinen, J.: Solid cores and solid hulls of weighted Bergman spaces. Banach J. Math. Anal. 13(2), 468–485 (2019)Bonet, J., Lusky, W., Taskinen, J.: On boundedness and compactness of Toeplitz operators in weighted $$H^{\infty }$$-spaces. J. Funct. Anal. 278(10), 108456 (2020)Bonet, J., Lusky, W., Taskinen, J.: On the boundedness of Toeplitz operators with radial symbols over weighted sup-norm spaces of holomorphic functions. J. Math. Anal. Appl. 493(1), 124515 (2021)Bonet, J., Lusky, W., Taskinen, J.: Unbounded Bergman projections on weighted spaces with respect to exponential weights. Integral Equ. Oper. Theory 93(6), 61 (2021)Bonet, J., Mangino, E.: Associated weights for spaces of p-integrable entire functions. Quaest. Math. 43(5–6), 747–760 (2020)Bonet, J., Mengestie, T., Worku, M.: Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces. Results Math. 74(4), 197 (2019)Bonet, J., Taskinen, J.: A note about Volterra operators on weighted Banach spaces of entire functions. Math. Nachr. 288(11–12), 1216–1225 (2015)Bonet, J., Taskinen, J.: Solid hulls of weighted Banach spaces of analytic functions on the unit disc with exponential weights. Ann. Acad. Sci. Fenn. 43, 521–530 (2018)Bonet, J., Taskinen, J.: Solid hulls of weighted Banach spaces of entire functions. Rev. Mat. Iberoam. 34(2), 593–608 (2018)Bonet, J., Vukotić, D.: Superposition operators between weighted Banach spaces of analytic functions of controlled growth. Monatsh. Math. 170(3–4), 311–323 (2013)Bonet, J., Vukotić, D.: A note on completeness of weighted normed spaces of analytic functions. Results Math. 72(1–2), 263–279 (2017)Bonet, J., Wolf, E.: A note on weighted Banach spaces of holomorphic functions. Arch. Math. 81, 650–654 (2003)Bourdon, P.S.: Essential angular derivatives and maximum growth of Koenigs eigenfunction. J. Funct. Anal. 160, 561–580 (1998)Bourdon, P.S.: Bellwethers for boundedness of composition operators on weighted Banach spaces of analytic functions. J. Aust. Math. Soc. 86(3), 305–314 (2009)Bourdon, P.S.: Invertible weighted composition operators. Proc. Am. Math. Soc. 142(1), 289–299 (2014)Boyd, C., Rueda, P.: Isometries between spaces of weighted holomorphic functions. Studia Math. 190(3), 203–231 (2009)Boyd, C., Rueda, P.: Isometries of weighted spaces of holomorphic functions on unbounded domains. Proc. R. Soc. Edinb. Sect. A 139(2), 253–271 (2009)Boyd, C., Rueda, P.: Holomorphic superposition operators between Banach function spaces. J. Aust. Math. Soc. 96(2), 186–197 (2014)Boyd, C., Rueda, P.: Superposition operators between weighted spaces of analytic functions. Quaest. Math. 36(3), 411–419 (2013)Boyd, C., Rueda, P.: Surjectivity of isometries between weighted spaces of holomorphic functions. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(3), 2461–2477 (2019)Bracci, F., Contreras, M.D., Díaz-Madrigal, S.: Continuous Semigroups of Holomorphic Self-maps of the Unit Disc. Springer, Berlin (2020)Carroll, T., Gilmore, C.: Weighted composition operators on Fock spaces and their dynamics. J. Math. Anal. Appl. 502(1), 125234 (2021)Carswell, B.J., MacCluer, B.D., Schuster, A.: Composition operators on the Fock space. Acta Sci. Math. (Szeged) 69, 871–887 (2003)Colonna, F., Martínez-Avendaño, R.A.: Hypercyclicity of composition operators on Banach spaces of analytic functions. Complex Anal. Oper. Theory 12(1), 305–323 (2018)Constantin, O.: A Volterra-type integration operator on Fock spaces. Proc. Am. Math. Soc. 140, 4247–4257 (2012)Constantin, O., Peláez, J.A.: Integral operators, embedding theorems and a Littlewood-Paley formula on weighted Fock spaces. J. Geom. Anal. 26(2), 1109–1154 (2016)Constantin, O., Peláez, J.A.: Boundedness of the Bergman projection on $$L^p$$-spaces with exponential weights. Bull. Sci. Math. 139, 245–268 (2015)Constantin, O., Persson, A.-M.: The spectrum of Volterra-type integration operators on generalized Fock spaces. Bull. Lond. Math. Soc. 47(6), 958–963 (2015)Contreras, M.D., Peláez, J.A., Pommerenke, C., Rättyä, J.: Integral operators mapping into the space of bounded analytic functions. J. Funct. Anal. 271, 2899–2943 (2016)Contreras, M.D., Hernández-Díaz, A.G.: Weighted composition operators in weighted Banach spaces of analytic functions. J. Aust. Math. Soc. 69, 41–60 (2000)Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton (1995)Dai, J.: Norm of the Hilbert matrix operator on the Korenblum space. J. Math. Anal. Appl. 514, 126270 (2022)Diamantopoulos, E., Siskakis, A.G.: Composition operators and the Hilbert matrix. Studia Math. 140(2), 191–198 (2000)Domański, P., Lindström, M.: Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions. Ann. Polon. Math. 79, 233–264 (2002)Domínguez, S., Girela, D.: Superposition operators between mixed norm spaces of analytic functions. Mediterr. J. Math. 18(1), 18 (2021)Dostanic, M.: Unboundedness of the Bergman projections on $$L^p$$ spaces with exponential weights. Proc. Edinb. Math. Soc. 47, 111–117 (2004)Doubtsov, E.: Integration and differentiation in Hardy growth spaces. Complex Anal. Oper. Theory 13(4), 1883–1893 (2019)Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory, 2nd Printing. Wiley Interscience Publ., New York (1964)Duren, P.L.: Theory of $$H^p$$ Spaces. Academic Press, New York (1970)Eklund, T., Galindo, P., Lindström, M.: Königs eigenfunction for composition operators on Bloch and $$H^\infty$$ type spaces. J. Math. Anal. Appl. 445(2), 1300–1309 (2017)Eklund, T., Galindo, P., Lindström, M., Nieminen, I.: Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions. J. Math. Anal. Appl. 451(1), 1–13 (2017)Eklund, T., Lindström, M., Pirasteh, M.M., Sanatpour, A.H., Wikman, N.: Generalized Volterra operators mapping between Banach spaces of analytic functions. Monatsh. Math. 189(2), 243–261 (2019)Fares, T., Lefèvre, P.: Nuclear composition operators on Bloch spaces. Proc. Am. Math. Soc. 148(6), 2487–2496 (2020)Galindo, P., Lindström, M.: Fredholm composition operators on analytic function spaces. Collect. Math. 63(2), 139–145 (2012)Galindo, P., Lindström, M.: Spectra of some weighted composition operators on dual Banach spaces of analytic functions. Integral Equ. Oper. Theory 90(3), 31 (2018)Galindo, P., Lindström, M., Wikman, N.: Spectra of weighted composition operators on analytic function spaces. Mediterr. J. Math. 17(1), 34 (2020)Gómez-Collado, M.C., Jornet, D.: Fredholm weighted composition operators on weighted Banach spaces of analytic functions of type $$H^\infty$$. J. Funct. Spaces 2015, 982135 (2015)Grosse-Erdmann, K., Peris, A.: Linear Chaos. Springer, London (2011)Guo, K., Izuchi, K.: Composition operators on Fock type space. Acta Sci. Math. (Szeged) 74, 807–828 (2008)Hai, P.V., Khoi, L.H.: Boundedness and compactness of weighted composition operators on Fock spaces $${\cal{F}}^p({\mathbb{C}})$$. Acta Math. Vietnam. 41(3), 531–537 (2016)Han, S.-A., Zhou, Z.-H.: Mean ergodicity of composition operators on Hardy space. Proc. Indian Acad. Sci. Math. Sci. 129(4), 45 (2019)Harutyunyan, A., Lusky, W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Studia Math. 184(3), 233–247 (2008)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Grad. Texts in Math., vol. 199. Springer, New York (2000)Heuser, H.R.: Functional Analysis. Wiley, New York (1982)Hu, Z.: Extended Cesàro operators on mixed-norm spaces. Proc. Am. Math. Soc. 131, 2171–2179 (2003)Hu, Z., Lv, X., Schuster, A.: Bergman spaces with exponential weights. J. Funct. Anal. 276, 1402–1429 (2019)Hyvärinen, O., Lindström, M., Nieminen, I., Saukko, E.: Spectra of weighted composition operators with automorphic symbols. J. Funct. Anal. 265(8), 1749–1777 (2013)Hyvärinen, O., Kemppainen, M., Lindström, M., Rautio, A., Saukko, E.: The essential norm of weighted composition operators on weighted Banach spaces of analytic functions. Integral Equ. Oper. Theory 72(2), 151–157 (2012)Jevtić, M., Vukotić, D., Arsenović, M.: Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces, RSME Springer Series, vol. 2. Springer, Berlin (2016)Jordá, E., Rodríguez-Arenas, A.: Ergodic properties of composition operators on Banach spaces of analytic functions. J. Math. Anal. Appl. 486(1), 123891 (2020)Karapetyants, A., Liflyand, E.: Defining Hausdorff operators on Euclidean spaces. Math. Methods Appl. Sci. 43(16), 9487–9498 (2020)Krengel, U.: Ergodic Theorems. de Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter Co., Berlin (1985)Liang, Y.-X., Zhou, Z.-H.: Hypercyclic behaviour of multiples of composition operators on weighted Banach spaces of holomorphic functions. Bull. Belg. Math. Soc. Simon Stevin 21(3), 385–401 (2014)Lin, Q.: Volterra type operators between Bloch type spaces and weighted Banach spaces. Integral Equ. Oper. Theory 91(2), 13 (2019)Lindström, M., Miihkinen, S., Wikman, N.: Norm estimates of weighted composition operators pertaining to the Hilbert matrix. Proc. Am. Math. Soc. 147(6), 2425–2435 (2019)Lindström, M., Miihkinen, S., Norrbo, D.: Exact essential norm of generalized Hilbert matrix operators on classical analytic functions spaces. Adv. Math. 408, 108598 (2022)Lusky, W.: On weighted spaces of harmonic and holomorphic functions. J. Lond. Math. Soc. 51, 309–320 (1995)Lusky, W.: On the Fourier series of unbounded harmonic functions. J. Lond. Math. Soc. 61(2), 568–580 (2000)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Studia Math. 175(1), 19–40 (2006)Malman, B.: Spectra of generalized Cesàro operators acting on growth spaces. Integral Equ. Oper. Theory 90(3), 26 (2018)Martín, M.J., Vukotić, D.: Isometries of the Bloch space among the composition operators. Bull. Lond. Math. Soc. 39(1), 151–155 (2007)Mas, A., Vukotić, D.: Invertible and isometric composition operators. Maediterr. J. Math. 19, 173 (2022)Meise, R., Vogt, D.: Introduction to Functional Analysis. Clarendon Press, Oxford University Press, New York (1997)Mengestie, T.: A note on the differential operator on generalized Fock spaces. J. Math. Anal. Appl. 458(2), 937–948 (2018)Mengestie, T.: On the spectrum of Volterra-type integral operators on Fock–Sobolev spaces. Complex Anal. Oper. Theory 11(6), 1451–1461 (2017)Mengestie, T., Ueki, S.-I.: Integral, differential and multiplication operators on generalized Fock spaces. Complex Anal. Oper. Theory 13(3), 935–958 (2019)Miralles, A., Wolf, E.: Hypercyclic composition operators on H0v-spaces. Math. Nachr. 286(1), 34–41 (2013)Mirotin, A.R.: Hausdorff operators on some spaces of holomorphic functions on the unit disc. Complex Anal. Oper. Theory 15, 85 (2021)Montes-Rodríguez, A.: Weighted composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. 61, 872–884 (2000)Nowak, M., Pavlovic, M.: On the Libera operator. J. Math. Anal. Appl. 370(2), 588–599 (2010)Pavlovic, M.: Definition and Properties of the Libera operators on mixed norm spaces. Sci. World J. 2014, 590656 (2014)Peláez, J.A., Rättyä, J.: Bergman projection induced by radial weight. Adv. Math. 391, 107950 (2021)Perfekt, K.-M.: Duality and distance formulas in spaces defined by means of oscillation. Ark. Mat. 51, 345–361 (2013)Perfekt, K.-M.: On M-ideals and $$o-O$$ type spaces. Math. Scand. 121(1), 151–160 (2017)Persson, A.-M.: On the spectrum of the Cesàro operator on spaces of analytic functions. J. Math. Anal Appl. 340, 1180–1203 (2008)Pommerenke, Ch.: Schlichte Funktionen un analytische Functionen von beschrnkter mittlerer Oszilation. Comment. Math. Helv. 52, 591–602 (1977)Ramos Fernández, J.C.: Bounded superposition operators between weighted Banach spaces of analytic functions. Appl. Math. Comput. 219(10), 4942–4949 (2013)Rudin, W.: Real and Complex Analysis. Mc Grawn Hill, New York (1974)Schindl, G.: S

The differentiation operator in the space of unifornly convergent Dirichlet series

This is the peer reviewed version of the following article: Bonet, J. The differentiation operator in the space of uniformly convergent Dirichlet series. Mathematische Nachrichten. 2020; 293: 1452-1458, which has been published in final form at https://doi.org/10.1002/mana.201900211. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.[EN] Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Frechet space of all Dirichlet series that are uniformly convergent in all half-planes {s is an element of C vertical bar Re s > epsilon} for each epsilon > 0. The properties of the formal inverse of the differentiation are also investigated.GeneralitatValenciana, Grant/Award Number: Prometeo/2017/102; Secretaria de Estado de Investigacion, Desarrollo e Innovacion, Grant/Award Number: MTM2016-76647-PBonet Solves, JA. (2020). The differentiation operator in the space of unifornly convergent Dirichlet series. Mathematische Nachrichten. 293(8):1452-1458. https://doi.org/10.1002/mana.201900211S145214582938Apostol, T. M. (1976). Introduction to Analytic Number Theory. Undergraduate Texts in Mathematics. doi:10.1007/978-1-4757-5579-4Bohr, H. (1913). Über die gleichmäßige Konvergenz Dirichletscher Reihen. Journal für die reine und angewandte Mathematik (Crelles Journal), 1913(143), 203-211. doi:10.1515/crll.1913.143.203Bonet, J. (2018). The Fréchet Schwartz Algebra of Uniformly Convergent Dirichlet Series. Proceedings of the Edinburgh Mathematical Society, 61(4), 933-942. doi:10.1017/s0013091517000438Bourdon, P. S., Feldman, N. S., & Shapiro, J. H. (2004). Some properties of N-supercyclic operators. Studia Mathematica, 165(2), 135-157. doi:10.4064/sm165-2-4Brevig, O. F., Perfekt, K.-M., & Seip, K. (2019). Volterra operators on Hardy spaces of Dirichlet series. Journal für die reine und angewandte Mathematik (Crelles Journal), 2019(754), 179-223. doi:10.1515/crelle-2016-0069Defant, A., García, D., Maestre, M., & Sevilla-Peris, P. (2011). Bohr’s strips for Dirichlet series in Banach spaces. Functiones et Approximatio Commentarii Mathematici, 44(2). doi:10.7169/facm/1308749122Defant, A., García, D., Maestre, M., & Sevilla-Peris, P. (2019). Dirichlet Series and Holomorphic Functions in High Dimensions. doi:10.1017/9781108691611Grosse-Erdmann, K.-G., & Peris Manguillot, A. (2011). Linear Chaos. Universitext. doi:10.1007/978-1-4471-2170-1Jarchow, H. (1981). Locally Convex Spaces. Mathematische Leitfäden. doi:10.1007/978-3-322-90559-8Krengel, U. (1985). Ergodic Theorems. doi:10.1515/9783110844641Queffélec, H. (2015). Espaces de séries de Dirichlet et leurs opérateurs de composition. Annales mathématiques Blaise Pascal, 22(S2), 267-344. doi:10.5802/ambp.351Queffélec, H., & Queffélec, M. (2013). Diophantine Approximation and Dirichlet Series. doi:10.1007/978-93-86279-61-

A note about the spectrum of composition operators induced by a rotation

[EN] A characterization of those points of the unit circle which belong to the spectrum of a composition operator C phi, defined by a rotation phi (z)=rz with |r|=1, on the space H0(D) of all analytic functions which vanish at 0, is given. Examples show that the spectrum of C phi need not be closed. In these examples the spectrum is dense but point 1 may or may not belong to it, and this is related to Diophantine approximation.The research of this paper was partially supported by the projects MTM2016-76647-P and GV Prometeo/2017/102.Bonet Solves, JA. (2020). A note about the spectrum of composition operators induced by a rotation. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-6. https://doi.org/10.1007/s13398-020-00788-5S161142Albanese, A.A., Bonet, J., Ricker, W.J.: Montel resolvents and uniformly mean ergodic semigroups of linear operators. Quaest. Math. 36, 253–290 (2013)Arendt, W., Celariès, B., Chalendar, I.: In Koenigs’ footsteps: diagonalization of composition operators. J. Funct. Anal. 278, 108313 (2020)Aron, R., Lindström, M.: Spectra of weighted composition operators on weighted Banach spaces of analytic functions. Israel J. Math. 141, 263–276 (2004)Bonet, J., Domanski, P.: A note on mean ergodic composition operators on spaces of holomorphic functions. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 105, 389–396 (2011)Carleson, L., Gamelin, T.W.: Complex Dynamics. Springer, New York (1993)Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton, FL (1995)Eisner, T., Farkas, B., Haase, M., Nagel, R.: Operator Theoretic Aspects of Ergodic Theory, Graduate Texts in Mathematics 272. Springer, New York (2015)Eklund, T., Lindström, M., Mleczko, P., Rzeczkowski, M.: Spectra of weighted composition operators on abstract Hardy spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113, 267–279 (2019)Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers, 6th edn. Oxford University Press, Oxford (2008)Ya, A.: Khinchin, Continued fractions. Translated from the third (1961) Russian edition. Reprint of the 1964 translation. Dover Publications, Inc., Mineola, NY (1997)Meise, R., Vogt, D.: Introduction to Functional Analysis. The Clarendon Press Oxford University Press, New York (1997)Queffélec, H., Queffélec, M.: Diophantine Approximation and Dirichlet series. Hindustain Book Agency, New Delhi (2013)Shapiro, J.H.: Composition Operators and Classical Function Theory. Springer, New York (1993)Shapiro, J.H.: Composition operators and Schröder’s functional equation. Contemporary Math. 213, 213–228 (1998)Vasilescu, F.H.: Analytic functional calculus and spectral decompositions. Translated from the Romanian. Mathematics and its Applications (East European Series), 1. D. Reidel Publishing Co., Dordrecht (1982

Chaos of the Differentiation Operator on Weighted Banach Spaces of Entire Functions

Motivated by recent work on the rate of growth of frequently hypercyclic entire functions due to Blasco, Grosse-Erdmann and Bonilla, we investigate conditions to ensure that the differentiation operator is chaotic or frequently hypercyclic on generalized weighted Bergman spaces of entire functions studied by Lusky, whenever the differentiation operator is continuous. As a consequence we partially complete the knowledge of possible rates of growth of frequently hypercyclic entire functions for the differentiation operator. © 2011 Springer Basel AG.J. Bonet is partially supported by MICINN and FEDER Projects MTM 2007-62643 and MTM2010-15200, GV Project Prometeo/2008/101 and UPV Project 2773. A. Bonilla is supported by MICINN and FEDER Project MTM2008-05891.Bonet Solves, JA.; Bonilla, A. (2013). Chaos of the Differentiation Operator on Weighted Banach Spaces of Entire Functions. Complex Analysis and Operator Theory. 7(1):33-42. https://doi.org/10.1007/s11785-011-0134-5S334271Bayart F., Grivaux S.: Hypercyclicité: le rôle du spectre ponctuel unimodulaire. C. R. Math. Acad. Sci. Paris 338, 703–708 (2004)Bayart F., Grivaux S.: Frequently hypercyclic operators. Trans. Am. Math. Soc. 358, 5083–5117 (2006)Bayart F., Matheron E.: Dynamics of Linear Operators, Cambridge Tracts in Mathematics, Vol. 179. Cambridge University Press, Cambridge (2009)Bernal-Gonz alez L., Bonilla A.: Exponential type of hypercyclic entire functions. Arch. Math. (Basel) 78, 283–290 (2002)Bierstedt K.D., Bonet J., Galbis A.: Weighted spaces of holomorphic functions on balanced domains. Mich. Math. J. 40, 271–297 (1993)Blasco O., Bonilla A., Grosse-Erdmann K.-G.: Rate of growth of frequently hypercyclic functions. Proc. Edinburgh Math. Soc. 53, 39–59 (2010)Bonilla A., Grosse-Erdmann K.-G.: On a theorem of Godefroy and Shapiro. Integr. Equa. Oper. Theory 56, 151–162 (2006)Bonilla, A., Grosse-Erdmann, K.-G.: Frequently hypercyclic operators and vectors, Ergodic Theory Dynam. Systems 27 (2007), 383–404. Erratum: Ergodic Theory Dynam. Systems 29 (6)(2009), 1993–1994Bonet J.: Dynamics of the differentiation operator on weighted spaces of entire functions. Math. Z. 261, 649–657 (2009)Grivaux, S.: A new class of frequently hypercyclic operators, with applications. to appear in Indiana Univ. Math. J.Grosse-Erdmann K.-G.: On the universal functions of G. R. MacLane. Complex Variables Theory Appl. 15, 193–196 (1990)Grosse-Erdmann K.-G.: Universal families and hypercyclic operators. Bull. Am. Math. Soc. (N.S.) 36, 345–381 (1999)Grosse-Erdmann K.-G.: Rate of growth of hypercyclic entire functions. Indag. Math. (N.S.) 11, 561–571 (2000)Grosse-Erdmann K.G.: Recent developments in hypercyclicity. Rev. R. Acad. Cien. Serie A Mat. 97, 273–286 (2003)Grosse-Erdmann K.G.: A weak criterion for vector-valued holomorphy. Math. Proc. Cambridge Philos. Soc. 136, 399–411 (2004)Grosse-Erdmann, K.G., Peris, A.: Linear Chaos. Springer, Berlin (to appear)Harutyunyan A., Lusky W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Stud. Math. 184, 233–247 (2008)Lusky W.: On generalized Bergman spaces. Stud. Math. 119, 77–95 (1996)Lusky W.: On the Fourier series of unbounded harmonic functions. J. Lond. Math. 61, 568–580 (2000)Lusky W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175, 19–45 (2006)MacLane G.R.: Sequences of derivatives and normal families. J. Anal. Math. 2, 72–87 (1952/53)Murray J.D.: Asymptotic Analysis. Springer, New York (1984)Shkarin S.A.: On the growth of D-universal functions. Univ. Math. Bull. 48(6), 49–51 (1993

Invariant subspaces of the integration operators on Hörmander algebras and Korenblum type spaces

[EN] We describe the proper closed invariant subspaces of the integration operator when it acts continuously on countable intersections and countable unions of weighted Banach spaces of holomorphic functions on the unit disc or the complex plane. Applications are given to the case of Korenblum type spaces and Hormander algebras of entire functions.This research was partially supported by the Projects MTM2016-76647-P and GV Prometeo/2017/102.Bonet Solves, JA.; Galbis, A. (2020). Invariant subspaces of the integration operators on Hörmander algebras and Korenblum type spaces. Integral Equations and Operator Theory. 92(4):1-13. https://doi.org/10.1007/s00020-020-02593-6S113924Abanin, A.V.: Effective and sampling sets for Hörmander spaces. Complex Anal. Oper. Theory 12(6), 1401–1419 (2018)Abanin, A.V., Tien, P.T.: Differentiation and integration operators on weighted Banach spaces of holomorphic functions. Math. Nachr. 290(8–9), 1144–1162 (2017)Abanin, A.V., Tien, P.T.: Invariant subspaces for classical operators on weighted spaces of holomorphic functions. Integr. Equ. Oper. Theory 89(3), 409–438 (2017)Abanin, A.V., Tien, P.T.: Compactness of classical operators on weighted Banach spaces of holomorphic functions. Collect. Math. 69(1), 1–15 (2018)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on Korenblum type spaces of analytic functions. Collect. Math. 69, 263–281 (2018)Aleman, A., Korenblum, B.: Volterra invariant subspaces of $$H^p$$. Bull. Sci. Math. 132, 510–528 (2008)Beltrán, M.J., Bonet, J., Fernández, C.: Classical operators on weighted Banach spaces of entire functions. Proc. Am. Math. Soc. 141(12), 4293–4303 (2013)Beltrán, M.J., Bonet, J., Fernández, C.: Classical operators on the Hörmander algebras. Discrete Contin. Dyn. Syst. 35(2), 637–652 (2015)Berenstein, C.A., Gay, R.: Complex Analysis and Special Topics in Harmonic Analysis. Springer, New York (1995)Berenstein, C.A., Li, B.Q., Vidras, A.: Geometric characterization of interpolating varieties for the (FN)-space $$A^0_p$$ of entire functions. Can. J. Math. 47, 28–43 (1995)Bierstedt, K.D., Bonet, J.: Some aspects of the modern theory of Fréchet spaces. RACSAM Rev. R. Acad. Cien. Serie A Mat. 97, 159–188 (2003)Bierstedt, K.D., Bonet, J.: Weighted (LB)-spaces of holomorphic functions: $$VH(G)=V_0H(G)$$ and completeness of $$V_0H(G)$$. J. Math. Anal. Appl. 323, 747–767 (2006)Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on bounded domains. Mich. Math. J. 40, 271–297 (1993)Bierstedt, K.D., Meise, R., Summers, W.H.: A projective description of weighted inductive limits. Trans. Am. Math. Soc. 272(1), 107–160 (1982)Bonet, J., Fernández, C.: The range of the restriction map for a multiplicity variety in Hörmander algebras of entire functions. Mediterr. J. Math. 11(2), 643–652 (2014)Bonet, J., Lusky, W., Taskinen, J.: Monomial basis in Korenblum type spaces of analytic functions. Proc. Am. Math. Soc. 146(12), 5269–5278 (2018)Constantin, O.: A Volterra-type integration operator on Fock spaces. Proc. Am. Math. Soc. 140, 4247–4257 (2012)Constantin, O., Peláez, J.A.: Integral operators, embedding theorems and a Littlewood–Paley formula on weighted Fock spaces. J. Geom. Anal. 26, 1109–1154 (2016)Douglas, R.G., Shapiro, H.S., Shields, A.L.: Cyclic vectors and invariant subspaces for the backward shift operator. Ann. Inst. Fourier 20, 37–76 (1970)Harutyunyan, A., Lusky, W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Studia Math. 184(3), 233–247 (2008)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Graduate Texts in Mathematics, vol. 199. Springer, New York (2000)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187–219 (1975)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Studia Math. 175, 19–45 (2006)Meise, R.: Sequence space representations for $$({\rm DFN})$$-algebras of entire functions modulo closed ideals. J. Reine Angew. Math. 363, 59–95 (1985)Meise, R., Taylor, B.A.: Sequence space representations for (FN)-algebras of entire functions modulo closed ideals. Studia Math. 85, 203–227 (1987)Meise, R., Vogt, D.: Introduction to Functional Analysis. Clarendon Press, Oxford University Press, New York (1997)Trèves, F.: Locally Convex Spaces and Linear Partial Differential Equations. Die Grundlehren der mathematischen Wissenschaften 146. Springer, New York (1967)Vogt, D.: Non-natural topologies on spaces of holomorphic functions. Ann. Polon. Math. 108(3), 215–217 (2013)Wolf, E.: Weighted Fréchet spaces of holomorphic functions. Studia Math. 174(3), 255–275 (2006)Zhu, K.: Operator Theory on Function Spaces. Mathematical Surveys and Monographs, vol. 138. American Mathematical Society, Providence (2007)Zhu, K.: Analysis on Fock Spaces. Graduate Texts in Mathematics, vol. 263. Springer, New York (2012