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

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