Coherent pairs of bivariate orthogonal polynomials

JOURNAL OF APPROXIMATION THEORY

卷:245

Article

Marcellan, Francisco^1,2  Marriaga, Misael E.³  Perez, Teresa E.^4,5  Pinar, Miguel A.^4,5 

[1] Univ Carlos III Madrid, Inst Ciencias Matemat ICMAT, Madrid, Spain

[2] Univ Carlos III Madrid, Dept Matemat, Madrid, Spain

[3] Univ Rey Juan Carlos, Dept Matemat Aplicada Ciencia & Ingn Mat & Tecnol, Madrid, Spain

[4] Univ Granada, Inst Matemat IEMath GR, Granada, Spain

[5] Univ Granada, Dept Matemat Aplicada, Fac Ciencias, Granada, Spain

关键词: Bivariate orthogonal polynomials;    Classical and semiclassical orthogonal polynomials;    Coherent pairs;   

DOI  :  10.1016/j.jat.2019.04.001

来源: Elsevier

【 摘 要 】

Coherent pairs of measures were introduced in 1991 and constitute a very useful tool in the study of Sobolev orthogonal polynomials on the real line. In this work, coherence and partial coherence in two variables appear as the natural extension of the univariate case. Given two families of bivariate orthogonal polynomials expressed as polynomial systems, they are a partial coherent pair if a polynomial of the second family can be given as a linear combination of the first partial derivatives of (at most) three consecutive polynomials of the first family. A full coherent pair is a pair of families of bivariate orthogonal polynomials related by means of partial coherent relations in each variable. Consequences of this kind of relations concerning both families of bivariate orthogonal polynomials are studied. Finally, some illustrative examples are provided. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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