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

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.


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