Functional Equations and Characterization Problems on Locally Compact Abelian Groups

  • Gennadiy Feldman

    B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences, Kharkov, Ukraine
Functional Equations and Characterization Problems on Locally Compact Abelian Groups cover
Buy from $74.00Download PDF

A subscription is required to access this book.

FrontmatterDownload pp. i–iv
PrefaceDownload pp. v–ix
ContentsDownload pp. xi–xii
IChapter I Preliminariesp. 1
1Locally compact Abelian groupspp. 1–11
2Probability distributions on locally compact Abelian groupspp. 11–18
IIChapter II Gaussian distributions on locally compact Abelian groupsp. 19
3Properties of Gaussian distributionspp. 19–32
4Cramér’s theorem on the decomposition of a Gaussian distribution on locally compact Abelian groupspp. 32–38
5Polynomials on locally compact Abelian groups and the Marcinkiewicz theorempp. 38–49
6Gaussian distributions in the sense of Urbanikpp. 49–55
IIIChapter III The Kac–Bernstein theorem for locally compact Abelian groupsp. 56
7Locally compact Abelian groups for which the Kac–Bernstein theorem holdspp. 56–68
8Random variables with values in the group R×T\mathbb{R}\times\mathbb{T} and in the aa-adic solenoid a\sum_app. 69–81
9Gaussian distributions in the sense of Bernsteinpp. 81–91
IVChapter IV The Skitovich–Darmois theorem for locally compact Abelian groups (the characteristic functions of random variables do not vanish)p. 92
10Locally compact Abelian groups for which the Skitovich–Darmois theorem holdspp. 92–107
11Random variables with values in the two-dimensional torus T2\mathbb{T}^2pp. 107–121
12Random variables with values in the groups R×T\mathbb{R}\times\mathbb{T} and a×T\sum_a\times\mathbb{T} pp. 121–132
VChapter V The Skitovich–Darmois theorem for locally compact Abelian groups (the general case)p. 133
13The number of random variables n=2n=2pp. 133–153
14The number of random variables n3n\ge 3pp. 153–172
15Random variables with values in the aa-adic solenoid a\sum_app. 172–185
VIChapter VI The Heyde theorem for locally compact Abelian groupsp. 186
16The characteristic functions of random variables do not vanishpp. 186–197
17Random variables with values in finite and discrete Abelian groupspp. 197–221
The Kac–Bernstein and Skitovich–Darmois functional equations on locally compact Abelian groupspp. 223–235
Comments and unsolved problemspp. 237–245
Bibliographypp. 247–252
Symbol indexpp. 253–254
Subject indexpp. 255–256

Supplementary Material