Generalized random fields of second order on locally compact groups. (Russian) Zbl 0577.60053

Ponomarenko, A. I.

Teor. Veroyatn. Mat. Stat. 29, 100-109 (1983).

Let \(\xi\) be a generalized random field of second order on an arbitrary, locally compact group G. It is shown that the correlation operator K of \(\xi\) is positively definite and selfadjoint. A representation of \(\xi\) in terms of K is given.
Some results are obtained about special classes of generalized fields of second order on G, like weakly homogeneous, almost weakly homogeneous and pseudohomogeneous fields.
Furthermore, the author shows that \(\xi\) may be decomposed into the sum of an (regular) orthogonal generalized field of second order on an open subset of G and a singular field. If \(\xi\) is left almost homogeneous, it may be decomposed into a sum of two left almost homogeneous fields on G, one of which is singular, the other regular.

Reviewer: C.Baldauf

MSC:

60G60	Random fields
60B15	Probability measures on groups or semigroups, Fourier transforms, factorization

Keywords:

generalized random field; locally compact group; correlation operator; homogeneous and pseudohomogeneous fields