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

L. Garza; J. Hernández; F. Marcellán

doi:10.1016/j.cam.2007.11.023

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

L. Garza, J. Hernández, F. Marcellán^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1220-1231
Number of pages	12
Journal	Journal of Computational and Applied Mathematics
Volume	233
Issue number	5
DOIs	https://doi.org/10.1016/j.cam.2007.11.023
Publication status	Published - 1 Jan 2010
Externally published	Yes

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2007.11.023

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AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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