## 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.

### 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