Direct and inverse spectral problems for block Jacobi type bounded symmetric matrices related to the two-dimensional real moment problem. (English) Zbl 1324.47033

Dudkin, Mykola E.; Kozak, Valentyna I.

Methods Funct. Anal. Topol. 20, No. 3, 219-251 (2014).

In the spirit of the connection between the classical moment problem and Jacobi matrices, the authors consider the two-dimensional moment problem and the related system of orthogonal polynomials with respect to a measure on \(\mathbb R^2\). The counterpart of a Jacobi matrix is a couple of block three-diagonal Jacobi type symmetric matrices generating symmetric operators in a space of \(l^2\) type. The authors study the case of bounded operators. This corresponds to measures of compact support.

Reviewer: Anatoly N. Kochubei (Kyïv)

MSC:

47A57	Linear operator methods in interpolation, moment and extension problems
44A60	Moment problems
42C05	Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

Keywords:

two-dimensional moment problem; orthogonal polynomials; Jacobi matrices