Spectral Methods in Infinite-Dimensional Analysis

Berezanskiĭ, I͡U. M., D. V. Malyshev, P. V. Malyshev, Y. G. Kondratiev

This major, two-volume work is devoted to the methods of the spectral theory of operators and the important role they play in infinite-dimensional analysis and its applications. Central to this study is the theory of the expansion of general eigenfunctions for families of commuting self-adjoint or normal operators. This enables a consideration of commutative models which can be applied to the representation of various commutation relations. Also included, for the first time in the literature, is an explanation of the theory of hypercomplex systems with locally compact bases. Applications to harmonic analysis lead to a study of the infinite-dimensional moment problem which is connected to problems of axiomatic field theory, integral representations of positive definite functions and kernels with an infinite number of variables. Infinite-dimensional elliptic differential operators are...