(1,1) - Coherent pairs on the unit circle

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dc.contributor.author Garza, Luis
dc.contributor.author Marcellán Español, Francisco José
dc.contributor.author Pinzón Cortés, Natalia Camila
dc.date.accessioned 2016-07-05T07:52:29Z
dc.date.available 2016-07-05T07:52:29Z
dc.date.issued 2013-01-01
dc.identifier.bibliographicCitation Abstract and Applied Analysis. Volume 2013, Article ID 307974, 8 pages
dc.identifier.issn 1085-3375
dc.identifier.uri http://hdl.handle.net/10016/23285
dc.description.abstract A pair (U,V) of Hermitian regular linear functionals on the unit circle is said to be a (1, 1)-coherent pair if their corresponding sequences of monic orthogonal polynomials {𝜙𝑛(𝑥)}𝑛≥0 and {𝜓𝑛(𝑥)}𝑛≥0 satisfy 𝜙[1] 𝑛 (𝑧) + 𝑎𝑛𝜙[1] 𝑛−1(𝑧) = 𝜓𝑛(𝑧) + 𝑏𝑛𝜓𝑛−1(𝑧), 𝑎𝑛 ≠ 0, 𝑛 ≥ 1, where 𝜙[1] 𝑛 (𝑧) = 𝜙󸀠 𝑛+1(𝑧)/(𝑛 + 1). In this contribution, we consider the cases when U is the linear functional associated with the Lebesgue and Bernstein-Szeg˝o measures, respectively, and we obtain a classification of the situations where V is associated with either a positive nontrivial measure or its rational spectral transformation.
dc.description.sponsorship The authors thank the referee the valuable comments. They greatly contributed to improve the contents of the paper. The work of Luis Garza was supported by Conacyt Grant no. 156668 and Beca Santander Iberoam´erica para J´ovenes Profesores e Investigadores (Mexico). The work of Francisco Marcell´an and Natalia C. Pinz´on-Cort´es has been supported by Direcci´on General de Investigaci´on, Desarrollo e Innovaci ´on, Ministerio de Econom´ıa y Competitividad of Spain, Grant MTM2012-36732-C03-01.
dc.format.extent 9
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Hindawi
dc.rights Atribución 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by/3.0/es/
dc.subject.other Sobolev orthogonal polynomials
dc.subject.other Delta-Coherent pairs
dc.subject.other n-Coherent Pairs
dc.subject.other Szego theory
dc.subject.other Extensions
dc.subject.other Respect
dc.title (1,1) - Coherent pairs on the unit circle
dc.type article
dc.relation.publisherversion http://dx.doi.org/10.1155/2013/307974
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1155/2013/307974
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM-2012-36732-C03-01.
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 1
dc.identifier.publicationlastpage 9
dc.identifier.publicationtitle Abstract and Applied Analysis.
dc.identifier.publicationvolume 2013
dc.identifier.uxxi AR/0000014290
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