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Unbounded commuting operators and multivariate orthogonal polynomials


Author: Yuan Xu
Journal: Proc. Amer. Math. Soc. 119 (1993), 1223-1231
MSC: Primary 47B25; Secondary 44A60, 47A57
MathSciNet review: 1165065
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Abstract: The multivariate orthogonal polynomials are related to a family of operators whose matrix representations are block Jacobi matrices. A sufficient condition is given so that these operators, in general unbounded, are commuting and selfadjoint. The spectral theorem for these operators is used to establish the existence of the measure of orthogonality in Favard's theorem.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1165065-7
Keywords: Multivariate orthogonal polynomials, recurrence relation, commuting selfadjoint operators, determinate measure
Article copyright: © Copyright 1993 American Mathematical Society