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 | References | Similar Articles | Additional Information

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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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1994-1211589-4

Keywords:
Three-term relation,
multivariate orthogonal polynomials,
associated polynomials

Article copyright:
© Copyright 1994
American Mathematical Society