65248 20220124163434.0 doi 10.1093/imrn/rnw186 sideral 104342 ART-2017-104342 eng Grünbaum, F.A. The CMV bispectral problem 2017 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/DGA/E64 info:eu-repo/grantAgreement/ES/MICINN/MTM2011-28952-C02-01 info:eu-repo/grantAgreement/ES/MINECO/MTM2014-53963-P info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 1.145 2017 MATHEMATICS 52 / 309 = 0.168 2017 Q1 T1 2.168 2017 Mathematics (miscellaneous) 2017 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Velázquez, L. Universidad de Zaragoza (orcid)0000-0002-3050-9540 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 2017, 19 (2017), 5833-5860 Int. math. res. not. INTERNATIONAL MATHEMATICS RESEARCH NOTICES 1073-7928 230663 http://zaguan.unizar.es/record/65248/files/texto_completo.pdf Versión publicada 72912 http://zaguan.unizar.es/record/65248/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:65248 articulos driver 2022-01-24-16:17:32 ARTICLE