Publication: Orthogonal polynomials and measures on the unit circle. The Geronimus transformations
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2010-01
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Elsevier
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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.
Description
12 pages, no figures.-- MSC2000 codes: 42C05, 15A23.-- Published in Special Issue dedicated to William B. Gragg on the occasion of his 70th birthday.
Keywords
Measures on the unit circle, Orthogonal polynomials, Spectral transformations, Hessenberg matrices
Bibliographic citation
Journal of Computational and Applied Mathematics, 2010, vol. 233, n. 5, p. 1220-1231