Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Solutions of three-term relations in several variables

Author: Yuan Xu
Journal: Proc. Amer. Math. Soc. 122 (1994), 151-155
MSC: Primary 33C50; Secondary 39A10, 41A05
MathSciNet review: 1211589
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Abstract: A system of multivariate orthogonal polynomials satisfies a matrix equation which plays the role of a three-term relation of the orthogonal polynomial of one variable. However, unlike the case of one variable, there does not exist a second solution of this matrix equation that is linearly independent to the orthogonal polynomials. In particular, there is no analogy of the associated polynomials in several variables.

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Keywords: Three-term relation, multivariate orthogonal polynomials, associated polynomials
Article copyright: © Copyright 1994 American Mathematical Society