Solutions of threeterm relations in several variables
Author:
Yuan Xu
Journal:
Proc. Amer. Math. Soc. 122 (1994), 151155
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 threeterm 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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 , Block Jacobi matrices and zeros of multivariate orthogonal polynomials, Trans. Amer. Math. Soc. (to appear). MR 1258289 (95g:42041)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199412115894
PII:
S 00029939(1994)12115894
Keywords:
Threeterm relation,
multivariate orthogonal polynomials,
associated polynomials
Article copyright:
© Copyright 1994 American Mathematical Society
