Christoffel transforms and Hermitian linear functionals

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Show simple item record Marcellán Español, Francisco José Hernández, Javier 2009-12-04T09:04:38Z 2009-12-04T09:04:38Z 2005-12
dc.identifier.bibliographicCitation Mediterranean Journal of Mathematics, 2005, vol. 2, n. 4, p. 451-458
dc.identifier.issn 1660-5446 (Print)
dc.identifier.issn 1660-5454 (Online)
dc.description 8 pages, no figures.-- MSC2000 codes: Primary 42C05; Secondary 15A23.
dc.description MR#: MR2192525 (2006h:42044)
dc.description Zbl#: Zbl 1121.42017
dc.description.abstract In this contribution we are focused on some spectral transformations of Hermitian linear functionals. They are the analogues of the Christoffel transform for linear functionals, i. e. for Jacobi matrices which has been deeply studied in the past. We consider Hermitian linear functionals associated with a probability measure supported on the unit circle. In such a case we compare the Hessenberg matrices associated with such a probability measure and its Christoffel transform. In this way, almost unitary matrices appear. We obtain the deviation to the unit matrix both for principal submatrices and the complete matrices respectively.
dc.description.sponsorship The work of the first author (F. Marcellán) was supported by Dirección General de Investigación, Ministerio de Educación y Ciencia of Spain, under grant BFM 2003-06335-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.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Birkhäuser Basel
dc.rights © Springer
dc.subject.other Hermitian linear functionals
dc.subject.other Christoffel transforms
dc.subject.other Laurent polynomials
dc.subject.other Orthogonal polynomials
dc.subject.other QR factorization
dc.title Christoffel transforms and Hermitian linear functionals
dc.type article PeerReviewed
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1007/s00009-005-0057-3
dc.rights.accessRights openAccess
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