On a spectral theorem in paraorthogonality theory

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dc.contributor.author Castillo Rodríguez, Kenier
dc.contributor.author Cruz Barroso, Ruymán
dc.contributor.author Perdomo Pío, Francisco
dc.date.accessioned 2016-07-05T08:31:41Z
dc.date.available 2016-07-05T08:31:41Z
dc.date.issued 2016-02
dc.identifier.bibliographicCitation Pacific Journal of Mathematics, February, v. 280, n.2, pp. 327-347.
dc.identifier.issn 0030-8730
dc.identifier.uri http://hdl.handle.net/10016/23287
dc.description.abstract Motivated by the works of Delsarte and Genin (1988, 1991), who studied paraorthogonal polynomials associated with positive definite Hermitian linear functionals and their corresponding recurrence relations, we provide paraorthogonality theory, in the context of quasidefinite Hermitian linear functionals, with a recurrence relation and the analogous result to the classical Favard's theorem or spectral theorem. As an application of our results, we prove that for any two monic polynomials whose zeros are simple and strictly interlacing on the unit circle, with the possible exception of one of them which could be common, there exists a sequence of paraorthogonal polynomials such that these polynomials belong to it. Furthermore, an application to the computation of Szegő quadrature formulas is also discussed.
dc.description.sponsorship The authors thank the referee for her/his valuable suggestions and comments which have contributed to improve the final form of this paper. The research of the first author is supported by the Portuguese Government through the Fundação para a Ciência e a Tecnologia (FCT) under the grant SFRH/BPD/101139/2014 and partially supported by the Brazilian Government through the CNPq under the project 470019/2013-1 and the Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of Spain under the project MTM2012–36732–C03–01. The work of the second and third authors is partially supported by Dirección General de Programas y Transferencia de Conocimiento, Ministerio de Ciencia e Innovación of Spain under the project MTM2011–28781.
dc.format.extent 24
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Mathematical Science Publishers
dc.rights Pacific Journal of Mathematics
dc.subject.other Paraorthogonal polynomials
dc.subject.other Quasidefinite Hermitian linear functionals
dc.subject.other Spectral theorem
dc.subject.other Geronimus Wendroff theorem
dc.subject.other Szego quadrature formulas
dc.title On a spectral theorem in paraorthogonality theory
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.2140/pjm.2016.280.327
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2012–36732–C03–01
dc.relation.projectID Gobierno de España. MTM2011–28781
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 327
dc.identifier.publicationissue 2
dc.identifier.publicationlastpage 347
dc.identifier.publicationtitle Pacific Journal of Mathematics
dc.identifier.publicationvolume 280
dc.identifier.uxxi AR/0000018005
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