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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Multivariate orthogonal polynomials and operator theory


Author: Yuan Xu
Journal: Trans. Amer. Math. Soc. 343 (1994), 193-202
MSC: Primary 42C05; Secondary 47A57, 47B15
MathSciNet review: 1169912
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Abstract: The multivariate orthogonal polynomials are related to a family of commuting selfadjoint operators. The spectral theorem for these operators is used to prove that a polynomial sequence satisfying a vector-matrix form of the three-term relation is orthonormal with a determinate measure.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1169912-X
PII: S 0002-9947(1994)1169912-X
Keywords: Multivariate orthogonal polynomials, recurrence relation, commuting selfadjoint operators, determinate measure
Article copyright: © Copyright 1994 American Mathematical Society