Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Heyde characterization theorem on compact totally disconnected and
  connected Abelian groups   By the well-known Heyde theorem, the Gaussian distribution on the real line
is characterized by the symmetry of the conditional distribution of one linear
form of independent random variables given another. In the case of two
independent random variables we give a complete description of compact totally
disconnected Abelian groups X, where an analogue of this theorem is valid. We
also prove that even a weak analogue of the Heyde theorem fails on compact
connected Abelian groups X. Coefficients of considered linear forms are
topological automorphisms of X. The proofs are based on the study of solutions
of a functional equation on the character group of the group X in the class of
Fourier transforms of probability distributions.

1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an