Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/5913

 Google™ Scholar. Others By: Marcellán, Francisco - Hernández, Javier
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 Title: Geronimus spectral transforms and measures on the complex plane Author(s): Marcellán, FranciscoHernández, Javier Publisher: Elsevier Issued date: Oct-2008 Citation: Journal of Computational and Applied Mathematics, 2008, vol. 219, n. 2, p. 441-456 URI: http://hdl.handle.net/10016/5913 ISSN: 0377-0427 DOI: 10.1016/j.cam.2007.06.017 Description: 16 pages, no figures.-- MSC2000 codes: 42C05; 15A23.MR#: MR2441238 (2009k:42053)Zbl#: Zbl 1149.42019 Abstract: We analyze a special spectral transform of a measure $\mu$ supported on a compact subset $C$ of the complex plane. A perturbation $\mu _{1}$ of $\mu$ is said to be a Geronimus spectral transform if d$\mu_1 = \frac {\text d \mu}{ -\alpha 2}$ where $\alpha \notin C$. We focus our attention in the analysis of the Hessenberg matrix associated with the multiplication operator in terms of the orthogonal polynomial basis defined by the measure $\mu _{1}$. Sponsor: The work of the first author (F. Marcellán) was supported by Dirección General de Investigación, Ministerio de Educación y Ciencia of Spain, under Grant MTM 2006-13000-C03-02, and INTAS Research Network NeCCA INTAS 03-51-6637. The work of the second author (J. Hernández) was supported by Fundación Universidad Carlos III de Madrid. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1016/j.cam.2007.06.017 Keywords: Hermitian linear functionalsChristoffel transformsGeronimus transformsUvarov transformsLaurent polynomialsOrthogonal polynomialsLU factorizationQR factorization Rights: © Elsevier Appears in Collections: DM - GAMA - Artículos de Revistas