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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

Location | Call Number | Status | Date Due |
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Salle R | 12358-01 / 43 FEL (Browse Shelf) | Available |

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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