Geronimus transformations of bivariate linear functionals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Marcellan, Francisco¹  Marriaga, Misael E.²  Perez, Teresa E.^3,4  Pinar, Miguel A.^3,4 

[1] Univ Carlos III Madrid, Dept Matemat, Getafe, Spain

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

[3] Univ Granada, Fac Ciencias, Inst Matemat IEMath GR, Granada, Spain

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

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

DOI  :  10.1016/j.jmaa.2019.123736

来源: Elsevier

【 摘 要 】

Given a linear functional u in the linear space of polynomials in two variables with real coefficients and a polynomial lambda(x, y), in this contribution we deal with Geronimus transformations of u, i.e., those linear functionals v such that u = lambda(x, y)v. The connection formulas between the sequences of bivariate orthogonal polynomials with respect to u and v are given. A matrix interpretation of such transformations by using LU and UL factorizations of the block Jacobi matrices associated with such polynomials is given. Finally, some illustrative examples of Geronimus transformations of weight function supported in domains of R-2 are discussed. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free