3,494 research outputs found
Dynamics and spectrum of the Cesà ro operator on C-infinity(R+)
[EN] The spectrum and point spectrum of the Cesaro averaging operator C acting on the Frechet space C-infinity(R+) of all C-infinity functions on the interval [0, infinity) are determined. We employ an approach via C-0-semigroup theory for linear operators. A spectral mapping theorem for the resolvent of a closed operator acting on a locally convex space is established; it constitutes a useful tool needed to establish the main result. The dynamical behaviour of C is also investigated.The research of the first two authors was partially supported by the projects MTM2013-43540-P, GVA Prometeo II/2013/013 and GVA ACOMP/2015/186 (Spain).Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2016). Dynamics and spectrum of the Cesà ro operator on C-infinity(R+). Monatshefte für Mathematik. 181:267-283. https://doi.org/10.1007/s00605-015-0863-zS267283181Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34, 401–436 (2009)Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic semigroups of operators. Rev. R. Acad. Cien. Serie A Mat. RACSAM 106, 299–319 (2012)Albanese, A.A., Bonet, J., Ricker, W.J.: Montel resolvents and uniformly mean ergodic semigroups of linear operators. Quaest. Math. 36, 253–290 (2013)Albanese, A.A., Bonet, J., Ricker, W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)Albanese, A.A., Bonet, J., Ricker, W.J.: Uniform mean ergodicity of C 0 -semigroups in a class of in Fréchet spaces. Funct. Approx. Comment. Math. 50, 307–349 (2014)Albanese, A.A., Bonet, J., Ricker, W.J.: On the continuous Cesà ro operator in certain function spaces. Positivity 19, 659–679 (2015)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesà ro operator in the Fréchet spaces ℓ p + and L p - . Glasgow Math. J. (accepted)Arendt, W.: Gaussian estimates and interpolation of the spectrum in L p . Diff. Int. Equ. 7, 1153–1168 (1994)Bayart, F., Matheron, E.: Dynamics of linear operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Boyd, D.W.: The spectrum of the Cesà ro operator. Acta Sci. Math. (Szeged) 29, 31–34 (1968)Grosse-Erdmann, K.G., Manguillot, A.P.: Linear chaos. Universitext, Springer Verlag, London (2011)Hille, E.: Remarks on ergodic theorems. Trans. Am. Math. Soc. 57, 246–269 (1945)Jarchow, H.: Locally convex spaces. Teubner, Stuttgart (1981)Komura, T.: Semigroups of operators in locally convex spaces. J. Funct. Anal. 2, 258–296 (1968)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Malgrange, B.: Idéaux de fonctions différentiables et division des distributions. Distributions, Editions École Polytechnique, Palaiseau, pp. 1–21 (2003)Meise, R., Vogt, D.: Introduction to functional analysis. Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press. Oxford University Press, New York (1997)Seeley, R.T.: Extension of C ∞ functions defined in a half space. Proc. Am. Math. Soc. 15, 625–626 (1964)Siskakis, A.G.: Composition semigroups and the Cesà ro operator. J. London Math. Soc. (2) 36, 153–164 (1987)Yosida, K.: Functional analysis. Springer, New York, Berlin, Heidelberg (1980)Valdivia, M.: Topics in locally convex spaces. North-Holland Math. Stud. 67, North-Holland, Amsterdam (1982
Large N reduction in the continuum three dimensional Yang-Mills theory
Numerical and theoretical evidence leads us to propose the following: Three
dimensional Euclidean Yang-Mills theory in the planar limit undergoes a phase
transition on a torus of side . For the planar limit is
-independent, as expected of a non-interacting string theory. We expect the
situation in four dimensions to be similar.Comment: 4 pages, latex file, two figures, version to appear in Phys. Rev.
Let
String Breaking in Non-Abelian Gauge Theories with Fundamental Matter Fields
We present clear numerical evidence for string breaking in three-dimensional
SU(2) gauge theory with fundamental bosonic matter through a mixing analysis
between Wilson loops and meson operators representing bound states of a static
source and a dynamical scalar. The breaking scale is calculated in the
continuum limit. In units of the lightest glueball we find . The implications of our results for QCD are discussed.Comment: 4 pages, 2 figures; equations (4)-(6) corrected, numerical results
and conclusions unchange
On the continuous Cesà ro operator in certain function spaces
“The final publication is available at Springer via http://dx.doi.org/10.1007/s11117-014-0321-5"Various properties of the (continuous) Cesà ro operator C, acting on Banach
and Fréchet spaces of continuous functions and L p-spaces, are investigated. For
instance, the spectrum and point spectrum of C are completely determined and a
study of certain dynamics of C is undertaken (eg. hyper- and supercyclicity, chaotic
behaviour). In addition, the mean (and uniform mean) ergodic nature of C acting in
the various spaces is identified.The research of the first two authors was partially supported by the projects MTM2010-15200 and GVA Prometeo II/2013/013 (Spain). The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2015). On the continuous Cesà ro operator in certain function spaces. Positivity. 19:659-679. https://doi.org/10.1007/s11117-014-0321-5S65967919Albanese, A.A.: Primary products of Banach spaces. Arch. Math. 66, 397–405 (1996)Albanese, A.A.: On subspaces of the spaces L loc p and of their strong duals. Math. Nachr. 197, 5–18 (1999)Albanese, A.A., Moscatelli, V.B.: Complemented subspaces of sums and products of copies of L 1 [ 0 , 1 ] . Rev. Mat. Univ. Complut. Madr. 9, 275–287 (1996)Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34, 401–436 (2009)Albanese, A.A., Bonet, J., Ricker, W.J.: On mean ergodic operators. In: Curbera, G.P. (eds.) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol. 201, pp. 1–20. Birkhäuser, Basel (2010)Albanese, A.A., Bonet, J., Ricker, W.J.: C 0 -semigroups and mean ergodic operators in a class of Fréchet spaces. J. Math. Anal. Appl. 365, 142–157 (2010)Albanese, A.A., Bonet, J., Ricker, W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)Bayart, F., Matheron, E.: Dynamics of linear operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Bellenot, S.F., Dubinsky, E.: Fréchet spaces with nuclear Köthe quotients. Trans. Am. Math. Soc. 273, 579–594 (1982)Bonet, J., Frerick, L., Peris, A., Wengenroth, J.: Transitive and hypercyclic operators on locally convex spaces. Bull. Lond. Math. Soc. 37, 254–264 (2005)Boyd, D.W.: The spectrum of the Cesà ro operator. Acta Sci. Math. (Szeged) 29, 31–34 (1968)Brown, A., Halmos, P.R., Shields, A.L.: Cesà ro operators. Acta Sci. Math. (Szeged) 26, 125–137 (1965)Dierolf, S., Zarnadze, D.N.: A note on strictly regular Fréchet spaces. Arch. Math. 42, 549–556 (1984)Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory (2nd Printing). Wiley-Interscience, New York (1964)Galaz Fontes, F., SolÃs, F.J.: Iterating the Cesà ro operators. Proc. Am. Math. Soc. 136, 2147–2153 (2008)Galaz Fontes, F., Ruiz-Aguilar, R.W.: Grados de ciclicidad de los operadores de Cesà ro–Hardy. Misc. Mat. 57, 103–117 (2013)González, M., León-Saavedra, F.: Cyclic behaviour of the Cesà ro operator on L 2 ( 0 , + ∞ ) . Proc. Am. Math. Soc. 137, 2049–2055 (2009)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear chaos. In: Universitext. Springer, London (2011)Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities. In: Reprint of the 1952 Edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1988)Krengel, U.: Ergodic theorems. In: De Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter Co., Berlin (1985)Leibowitz, G.M.: Spectra of finite range Cesà ro operators. Acta Sci. Math. (Szeged) 35, 27–28 (1973)Leibowitz, G.M.: The Cesà ro operators and their generalizations: examples in infinite-dimensional linear analysis. Am. Math. Mon. 80, 654–661 (1973)León-Saavedra, F., Piqueras-Lerena, A., Seoane-Sepúlveda, J.B.: Orbits of Cesà ro type operators. Math. Nachr. 282, 764–773 (2009)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Meise, R., Vogt, D.: Introduction to functional analysis. In: Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press; Oxford University Press, New York (1997)Metafune, G., Moscatelli, V.B.: Quojections and prequojections. In: TerzioÄŸlu, T. (ed.) Advances in the Theory of Fréchet spaces. NATO ASI Series, vol. 287, pp. 235–254. Kluwer Academic Publishers, Dordrecht (1989)Moscatelli, V.B.: Fréchet spaces without norms and without bases. Bull. Lond. Math. Soc. 12, 63–66 (1980)Piszczek, K.: Quasi-reflexive Fréchet spaces and mean ergodicity. J. Math. Anal. Appl. 361, 224–233 (2010)Piszczek, K.: Barrelled spaces and mean ergodicity. Rev R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 104, 5–11 (2010)Yosida, K.: Functional Analysis, 6th edn. Springer, Berlin (1980
Lunar laser ranging in infrfared at hte Grasse laser station
For many years, lunar laser ranging (LLR) observations using a green
wavelength have suffered an inhomogeneity problem both temporally and
spatially. This paper reports on the implementation of a new infrared detection
at the Grasse LLR station and describes how infrared telemetry improves this
situation. Our first results show that infrared detection permits us to densify
the observations and allows measurements during the new and the full Moon
periods. The link budget improvement leads to homogeneous telemetric
measurements on each lunar retro-reflector. Finally, a surprising result is
obtained on the Lunokhod 2 array which attains the same efficiency as Lunokhod
1 with an infrared laser link, although those two targets exhibit a
differential efficiency of six with a green laser link
Another determination of the quark condensate from an overlap action
I use the technique of Hernandez, et al (hep-lat/0106011) to convert a recent
calculation of the lattice-regulated quark condensate from an overlap action to
a continuum-regulated number. I find Sigma(MSbar)(mu = 2 GeV) = (282(6)
MeV)-cubed times (a-inverse/1766 MeV)-cubed from a calculation with the Wilson
gauge action at beta=5.9.Comment: 3 pages, Revtex, 1 postscript figure. References added. COLO-HEP-47
The Spatial String Tension in the Deconfined Phase of the (3+1)-Dimensional SU(2) Gauge Theory
We present results of a detailed investigation of the temperature dependence
of the spatial string tension in SU(2) gauge theory. We show, for the first
time, that the spatial string tension is scaling on the lattice and thus is
non-vanishing in the continuum limit. It is temperature independent below Tc
and rises rapidly above. For temperatures larger than 2Tc we find a scaling
behaviour consistent with sigma_s(T) = 0.136(11) g^4(T) T^2, where g(T) is the
2-loop running coupling constant with a scale parameter determined as Lambda_T
= 0.076(13) Tc.Comment: 8 pages (Latex, shell archive, 3 PostScript figures), HLRZ-93-43,
BI-TP 93/30, FSU-SCRI-93-76, WUB 93-2
Financial instability from local market measures
We study the emergence of instabilities in a stylized model of a financial
market, when different market actors calculate prices according to different
(local) market measures. We derive typical properties for ensembles of large
random markets using techniques borrowed from statistical mechanics of
disordered systems. We show that, depending on the number of financial
instruments available and on the heterogeneity of local measures, the market
moves from an arbitrage-free phase to an unstable one, where the complexity of
the market - as measured by the diversity of financial instruments - increases,
and arbitrage opportunities arise. A sharp transition separates the two phases.
Focusing on two different classes of local measures inspired by real markets
strategies, we are able to analytically compute the critical lines,
corroborating our findings with numerical simulations.Comment: 17 pages, 4 figure
Three-Quark Potential in SU(3) Lattice QCD
The static three-quark (3Q) potential is measured in the SU(3) lattice QCD
with and at the quenched level. From the 3Q Wilson
loop, the 3Q ground-state potential is extracted using the
smearing technique for the ground-state enhancement. With accuracy better than
a few %, is well described by a sum of a constant, the two-body
Coulomb term and the three-body linear confinement term , where denotes the minimal length of the color flux tube
linking the three quarks. By comparing with the Q- potential, we
find a universal feature of the string tension, , as well as the one-gluon-exchange result for the
Coulomb coefficient, .Comment: 7 pages, 3 figur
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