Orthogonal polynomials and measures on the unit circle. The Geronimus transformations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article

Garza, L.¹  Hernandez, J.¹  Marcellan, F.¹ 

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

关键词: Measures on the unit circle;    Orthogonal polynomials;    Spectral transformations;    Hessenberg matrices;   

DOI  :  10.1016/j.cam.2007.11.023

来源: Elsevier

【 摘 要 】

In this paper we analyze a perturbation of a nontrivial positive measure supported on the unit circle. This perturbation is the inverse of the Christoffel transformation and is called the Geronimus transformation. We study the corresponding sequences of monic orthogonal polynomials as well as the connection between the associated Hessenberg matrices. Finally, we show an example of this kind of transformation. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free