Block Jacobi matrices and zeros of multivariate orthogonal polynomials

Xu, Yuan

doi:10.1090/S0002-9947-1994-1258289-7

Block Jacobi matrices and zeros of multivariate orthogonal polynomials
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Trans. Amer. Math. Soc. 342 (1994), 855-866 Request permission

Abstract:

A commuting family of symmetric matrices are called the block Jacobi matrices, if they are block tridiagonal. They are related to multivariate orthogonal polynomials. We study their eigenvalues and joint eigenvectors. The joint eigenvalues of the truncated block Jacobi matrices correspond to the common zeros of the multivariate orthogonal polynomials.

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