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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Block Jacobi matrices and zeros of multivariate orthogonal polynomials


Author: Yuan Xu
Journal: Trans. Amer. Math. Soc. 342 (1994), 855-866
MSC: Primary 42C05; Secondary 65D99, 65F99
MathSciNet review: 1258289
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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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DOI: https://doi.org/10.1090/S0002-9947-1994-1258289-7
Keywords: Block Jacobi matrices, truncated block Jacobi matrices, joint eigenvectors, common zeros of multivariate orthogonal polynomials, commuting selfadjoint operators
Article copyright: © Copyright 1994 American Mathematical Society