Spectral theory of self-adjoint operators, and infinite-dimensional analysis

In this paper we give a survey of results on some problems of the spectral theory of self-adjoint operators, closely connected with infinite-dimensional analysis. The following questions are considered: expansions in eigenfunctions of families of commuting self-adjoint operators, with applications to the derivation of representations of positive definite kernels in the form of continual integrals; and spectral analysis of self-adjoint operators acting on spaces of functions of an infinite-dimensional argument.