425 research outputs found
The Bohr radius of the -dimensional polydisk is equivalent to
We show that the Bohr radius of the polydisk behaves
asymptotically as . Our argument is based on a new
interpolative approach to the Bohnenblust--Hille inequalities which allows us
to prove that the polynomial Bohnenblust--Hille inequality is subexponential.Comment: The introduction was expanded and some misprints correcte
On the minimal number of matrices which form a locally hypercyclic, non-hypercyclic tuple
In this paper we extend the notion of a locally hypercyclic operator to that
of a locally hypercyclic tuple of operators. We then show that the class of
hypercyclic tuples of operators forms a proper subclass to that of locally
hypercyclic tuples of operators. What is rather remarkable is that in every
finite dimensional vector space over or , a pair of
commuting matrices exists which forms a locally hypercyclic, non-hypercyclic
tuple. This comes in direct contrast to the case of hypercyclic tuples where
the minimal number of matrices required for hypercyclicity is related to the
dimension of the vector space. In this direction we prove that the minimal
number of diagonal matrices required to form a hypercyclic tuple on
is , thus complementing a recent result due to Feldman.Comment: 15 pages, title changed, section for infinite dimensional spaces
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Impact of pump OSNR on noise figure for fiber-optical parametric amplifiers
Electrical measurements of the noise figure of a fiberoptical parametric amplifier are presented and compared with optical measurements. The transfer of pump noise by four-wave mixing was clearly demonstrated. A numerical model was developed to simulate the transfer of pump noise and validated by these measurements. Using this model, we determine, for practical systems, a minimum required pump optical signal-to-noise ratio of 65 dB
Impact of pump phase modulation on system performance of fibre-optical parametric amplifiers
Bit error rate induced in a parametric amplifier has been measured with a 10 Gbit=s line rate. It is shown experimentally that the phase modulation of the pump distorts the mark level of the channel and may cause system penalty. Different phase modulation schemes have been compared
Almost sure-sign convergence of Hardy-type Dirichlet series
[EN] Hartman proved in 1939 that the width of the largest possible strip in the complex plane on which a Dirichlet series is uniformly a.s.- sign convergent (i.e., converges uniformly for almost all sequences of signs epsilon (n) = +/- 1) but does not convergent absolutely, equals 1/2. We study this result from a more modern point of view within the framework of so-called Hardytype Dirichlet series with values in a Banach space.Supported by CONICET-PIP 11220130100329CO, PICT 2015-2299 and UBACyT 20020130100474BA.
Supported by MICINN MTM2017-83262-C2-1-P.
Supported by MICINN MTM2017-83262-C2-1-P and UPV-SP20120700.Carando, D.; Defant, A.; Sevilla Peris, P. (2018). Almost sure-sign convergence of Hardy-type Dirichlet series. Journal d Analyse MathĂ©matique. 135(1):225-247. https://doi.org/10.1007/s11854-018-0034-yS2252471351A. Aleman, J.-F. Olsen, and E. Saksman, Fourier multipliers for Hardy spaces of Dirichlet series, Int. Math. Res. Not. IMRN 16 (2014), 4368â4378.R. Balasubramanian, B. Calado, and H. QueffĂ©lec, The Bohr inequality for ordinary Dirichlet series Studia Math. 175 (2006), 285â304.F. Bayart, Hardy spaces of Dirichlet series and their composition operators, Monatsh. Math. 136 (2002), 203â236.F. Bayart, A. Defant, L. Frerick, M. Maestre, and P. Sevilla-Peris, Monomial series expansion of Hp-functions and multipliers ofHp-Dirichlet series, Math. Ann. 368 (2017), 837â876.F. Bayart, D. Pellegrino, and J. B. Seoane-SepĂșlveda, The Bohr radius of the n-dimensional polydisk is equivalent to ( log n ) / n , Adv. Math. 264 (2014), 726â746.F. Bayart, H. QueffĂ©lec, and K. Seip, Approximation numbers of composition operators on Hp spaces of Dirichlet series, Ann. Inst. Fourier (Grenoble) 66 (2016), 551â588.H. F. Bohnenblust and E. Hille. On the absolute convergence of Dirichlet series, Ann. of Math. (2) 32 (1931), 600â622.H. Bohr, Ăber die Bedeutung der Potenzreihen unendlich vieler Variablen in der Theorie der Dirichletâschen Reihen â a n n s , Nachr. Ges.Wiss. Göttingen, Math. Phys. Kl., 1913, pp. 441â488.D. Carando, A. Defant, and P. Sevilla-Peris, Bohrâs absolute convergence problem for Hp- Dirichlet series in Banach spaces, Anal. PDE 7 (2014), 513â527.D. Carando, A. Defant, and P. Sevilla-Peris, Some polynomial versions of cotype and applications, J. Funct. Anal. 270 (2016), 68â87.B. J. Cole and T. W. Gamelin, Representing measures and Hardy spaces for the infinite polydisk algebra, Proc. London Math. Soc. (3) 53 (1986), 112â142.R. de la BretĂšche. Sur lâordre de grandeur des polynĂŽmes de Dirichlet, Acta Arith. 134 (2008), 141â148.A. Defant, L. Frerick, J. Ortega-CerdĂ , M. OunĂ€ies, and K. Seip, The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive, Ann. of Math. (2) 174 (2011), 485â497.A. Defant, D. GarcĂa, M. Maestre, and D. PĂ©rez-GarcĂa, Bohrâs strip for vector valued Dirichlet series, Math. Ann. 342 (2008), 533â555.A. Defant, M. Maestre, and U. Schwarting, Bohr radii of vector valued holomorphic functions, Adv. Math. 231 (2012), 2837â2857.A. Defant and A. PĂ©rez, Hardy spaces of vector-valued Dirichlet series, StudiaMath. (to appear), 2018 DOI: 10.4064/sm170303-26-7.A. Defant, U. Schwarting, and P. Sevilla-Peris, Estimates for vector valued Dirichlet polynomials, Monatsh. Math. 175 (2014), 89â116.J. Diestel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge University Press, Cambridge, 1995.P. Hartman, On Dirichlet series involving random coefficients, Amer. J. Math. 61 (1939), 955â964.H. Hedenmalm, P. Lindqvist, and K. Seip, A Hilbert space of Dirichlet series and systems of dilated functions in L2(0, 1), Duke Math. J. 86 (1997), 1â37.A. Hildebrand, and G. Tenenbaum, Integers without large prime factors, J. Thor. Nombres Bordeaux 5 (1993), 411â484.S. V. Konyagin and H. QueffĂ©lec, The translation 1/2 in the theory of Dirichlet series, Real Anal. Exchange 27 (2001/02) 155â175.J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. II, Springer-Verlag, Berlin, 1979.B. Maurizi and H. QueffĂ©lec, Some remarks on the algebra of bounded Dirichlet series, J. Fourier Anal. Appl. 16 (2010), 676â692.H. QueffĂ©lec, H. Bohrâs vision of ordinary Dirichlet series; old and new results, J. Anal. 3 (1995), 43â60.H. QueffĂ©lec and M. QueffĂ©lec, Diophantine Approximation and Dirichlet Series, Hindustan Book Agency, New Delhi, 2013.G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press, Cambridge, 1995
A note on abscissas of Dirichlet series
[EN] We present an abstract approach to the abscissas of convergence of vector-valued Dirichlet series. As a consequence we deduce that the abscissas for Hardy spaces of Dirichlet series are all equal. We also introduce and study weak versions of the abscissas for scalar-valued Dirichlet series.A. Defant: Partially supported by MINECO and FEDER MTM2017-83262-C2-1-P.
A. PĂ©rez: Supported by La Caixa Foundation, MINECO and FEDER MTM2014-57838-C2-1-P and
FundaciĂłn SĂ©neca - RegiĂłn de Murcia (CARM 19368/PI/14).
P. Sevilla-Peris: Supported by MINECO and FEDER MTM2017-83262-C2-1-P.Defant, A.; PĂ©rez, A.; Sevilla Peris, P. (2019). A note on abscissas of Dirichlet series. Revista de la Real Academia de Ciencias Exactas FĂsicas y Naturales Serie A MatemĂĄticas. 113(3):2639-2653. https://doi.org/10.1007/s13398-019-00647-yS263926531133Bayart, F.: Hardy spaces of Dirichlet series and their composition operators. Mon. Math. 136(3), 203â236 (2002)Bohnenblust, H.F., Hille, E.: On the absolute convergence of Dirichlet series. Ann Math. 32(3), 600â622 (1931)Bohr, H.: Ăber die Bedeutung der Potenzreihen unendlich vieler Variablen in der Theorie der Dirichletâschen Reihen â a n n s . Nachr. Ges. Wiss. Göttingen, Math. Phys. Kl., pp. 441â488 (1913)Bonet, J.: Abscissas of weak convergence of vector valued Dirichlet series. J. Funct. Anal. 269(12), 3914â3927 (2015)Carando, D., Defant, A., Sevilla-Peris, P.: Bohrâs absolute convergence problem for H p -Dirichlet series in Banach spaces. Anal. PDE 7(2), 513â527 (2014)Carando, D., Defant, A., Sevilla-Peris, P.: Some polynomial versions of cotype and applications. J. Funct. Anal. 270(1), 68â87 (2016)Defant, A., GarcĂa, D., Maestre, M., PĂ©rez-GarcĂa, D.: Bohrâs strip for vector valued Dirichlet series. Math. Ann. 342(3), 533â555 (2008)Defant, A., GarcĂa, D., Maestre, M., SevillaâPeris, P.: Dirichlet Series and Holomorphic Funcions in High Dimensions, vol. 37 of New Mathematical Monographs. Cambridge University Press, Cambridge (2019)Defant, A., PĂ©rez, A.: Optimal comparison of the p -norms of Dirichlet polynomials. Israel J. Math. 221(2), 837â852 (2017)Defant, A., PĂ©rez, A.: Hardy spaces of vector-valued Dirichlet series. Studia Math. 243(1), 53â78 (2018)Diestel, J., Jarchow, H., Tonge, A.: Absolutely summing operators, vol. 43 of Cambridge studies in advanced mathematics. Cambridge University Press, Cambridge (1995)Maurizi, B., QueffĂ©lec, H.: Some remarks on the algebra of bounded Dirichlet series. J. Fourier Anal. Appl. 16(5), 676â692 (2010)QueffĂ©lec, H., QueffĂ©lec, M.: Diophantine approximation and Dirichlet series, vol. 2 of HarishâChandra research institute lecture notes. Hindustan Book Agency, New Delhi (2013
Hypercyclic algebras for convolution and composition operators
[EN] We provide an alternative proof to those by Shkarin and by Bayart and Matheron that the operator D of complex differentiation supports a hypercyclic algebra on the space of entire functions. In particular we obtain hypercyclic algebras for many convolution operators not induced by polynomials, such as , , or , where . In contrast, weighted composition operators on function algebras of analytic functions on a plane domain fail to support supercyclic algebras.This work is supported in part by MEC, Project MTM 2016-7963-P. We also thank Angeles Prieto for comments and suggestions.BĂšs, J.; Conejero, JA.; Papathanasiou, D. (2018). Hypercyclic algebras for convolution and composition operators. Journal of Functional Analysis. 274(10):2884-2905. https://doi.org/10.1016/j.jfa.2018.02.003S288429052741
Securitization outside of the West:conceptualizing the securitizationâneo-patrimonialism nexus in Africa
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