Functional equations and characterization problems on locally compact Abelian groups / Gennadiy Feldman

Auteur: Feldman, Gennadiy Mikhailovich (1947-) - AuteurType de document: MonographieCollection: EMS Tracts in mathematics ; 5Langue: anglaisPays: SwisseÉditeur: Zurich : European Mathematical Society, 2008Description: 1 vol. (XII-256 p.) ; 25 cm ISBN: 9783037190456 ; rel. Note: The emphasis of this monograph is laid on ‘classical’ characterizations of Gaussian laws on the real line resp. on finite dimensional vector spaces and the possibility of extensions to locally compact abelian groups. In fact, there exist various characterizations of Gaussian laws, the characterizing properties are all equivalent in the ‘classical’ setup. But even for the torus many of these properties are known to be not equivalent. Therefore, on general abelian groups, we have various definitions of Gaussian laws. Hence natural questions arise: E.g., describe the class of locally compact groups on which the properties under consideration are equivalent with a given definition of Gaussian laws. ... (Zentralblatt)Bibliographie: Bibliogr. p. [247]-252. Index. Sujets MSC: 43A25 Abstract harmonic analysis -- Abstract harmonic analysis -- Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
43A05 Abstract harmonic analysis -- Abstract harmonic analysis -- Measures on groups and semigroups, etc
43A35 Abstract harmonic analysis -- Abstract harmonic analysis -- Positive definite functions on groups, semigroups, etc
60B15 Probability theory and stochastic processes -- Probability theory on algebraic and topological structures -- Probability measures on groups or semigroups, Fourier transforms, factorization
62E10 Statistics -- Distribution theory -- Characterization and structure theory
En-ligne: Zentralblatt | MathSciNet
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The emphasis of this monograph is laid on ‘classical’ characterizations of Gaussian laws on the real line resp. on finite dimensional vector spaces and the possibility of extensions to locally compact abelian groups. In fact, there exist various characterizations of Gaussian laws, the characterizing properties are all equivalent in the ‘classical’ setup. But even for the torus many of these properties are known to be not equivalent. Therefore, on general abelian groups, we have various definitions of Gaussian laws. Hence natural questions arise: E.g., describe the class of locally compact groups on which the properties under consideration are equivalent with a given definition of Gaussian laws. ... (Zentralblatt)

Bibliogr. p. [247]-252. Index

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