The CMV bispectral problem
Resumen: A classical result due to Bochner classifies the orthogonal polynomials on the real line which are common eigenfunctions of a second order linear differential operator. We settle a natural version of the Bochner problem on the unit circle which answers a similar question concerning orthogonal Laurent polynomials and can be formulated as a bispectral problem involving CMV matrices. We solve this CMV bispectral problem in great generality proving that, except the Lebesgue measure, no other one on the unit circle yields a sequence of orthogonal Laurent polynomials which are eigenfunctions of a linear differential operator of arbitrary order. Actually, we prove that this is the case even if such an eigenfunction condition is imposed up to finitely many orthogonal Laurent polynomials.
Idioma: Inglés
DOI: 10.1093/imrn/rnw186
Año: 2017
Publicado en: INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2017, 19 (2017), 5833-5860
ISSN: 1073-7928

Factor impacto JCR: 1.145 (2017)
Categ. JCR: MATHEMATICS rank: 52 / 309 = 0.168 (2017) - Q1 - T1
Factor impacto SCIMAGO: 2.168 - Mathematics (miscellaneous) (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E64
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2011-28952-C02-01
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2014-53963-P
Tipo y forma: Article (Published version)
Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)

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