On the strong matrix Hamburger moment problem

Abstract

517.948We obtain necessary and sufficient conditions for the solvability of the strong matrix Hamburger moment problem. We describe all solutions of the moment problem by using the fundamental results of A. V. Shtraus on generalized resolvents of symmetric operators.

The Nevanlinna-Pick matrix interpolation in the Carathéodory class with infinite data both in the nondegenerate and degenerate cases

“…where R z (A) is a generalized resolvent of A (which corresponds to A). Therefore T (z) has a representation of the form (15).…”

“…In order to obtain an analytic description of solutions, we shall use important results of Chumakin on generalized resolvents of isometric operators [12], [13]. A similar approach was recently used in [14], [15], [16] to treat various matrix moment problems. Also, the necessary and sufficient conditions for the determinacy of the problem (1) are obtained.…”

Truncated matrix trigonometric problem of moments: operator approach

“…The operator approach enables one to study both the nondegenerate and degenerate cases for various problems of moments (see [11] and also [12,13]). Note that this approach is close to the "pure operator" approach applied by Sz.-Nagy and Korányi to the Nevanlinna-Pick interpolation problem [1, p. 217].…”

The strong matrix Stieltjes moment problem

“…The scalar (N = 1) strong matrix Hamburger moment problem has been intensively studied since 1980-th, see a survey [7], a recent paper [10] and References therein. For the matrix case, see papers [11], [12] and papers cited there.…”