Integral representation of kernels invariant with respect to local semigroups of isometries and generalization of the Krein - Schwartz theorem.

Abstract

tWe show that the theory of local semigroups of isometric operators leads to a generalization of the Krein-Berezanski-Korsunski decomposition of invariant kernels, which allows to extend the Bochner-Schwartz and the Krein-Schwartz theoremo generalized Toeplitz kernels.