Multiple Geronimus transformations

被引：21

作者：

Derevyagin, M. ^{[1
]}

Garcia-Ardila, J. C. ^{[2
]}

Marcellan, F. ^{[2
,3
]}

机构：

[1] Katholieke Univ Leuven, Dept Math, BE-3001 Heverlee, Belgium

[2] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain

[3] Inst Ciencias Matemat ICMAT, Madrid, Spain

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 454卷

关键词：

Orthogonal polynomials; Geronimus transformation; Sobolev inner products; Cholesky decomposition; Jacobi matrix; Band matrix; ORTHOGONAL POLYNOMIALS; DARBOUX TRANSFORMATIONS; INVERSE PROBLEM; PRODUCT; FUNCTIONALS; MATRICES; FORM;

D O I：

10.1016/j.laa.2014.04.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider multiple Geronimus transformations and show that they lead to discrete (non-diagonal) Sobolev type inner products. Moreover, it is shown that every discrete Sobolev inner product can be obtained as a multiple Geronimus transformation. A connection with Geronimus spectral transformations for matrix orthogonal polynomials is also considered. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：158 / 183

页数：26

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