Matrix orthogonal Laurent polynomials on the unit circle and Toda type integrable systems

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Show simple item record Ariznabarreta, Gerardo Mañas, Manuel 2016-07-20T09:48:19Z 2016-11-01T23:00:09Z 2014-10-20
dc.identifier.bibliographicCitation Advances in Mathematics, 2014, v. 264, pp. 396-463
dc.description.abstract of Toda-like integrable systems are connected us-ing the Gauss-Borel factorization of two, left and a right, Cantero-Morales-Velázquez block moment matrices, which are constructed using a quasi-definite matrix measure. Ablock Gauss-Borel factorization problem of these moment matrices leads to two sets of biorthogonal matrix orthogonal Laurent polynomials and matrix Szegő polynomials, which can be expressed in terms of Schur complements of bordered trun-cations of the block moment matrix. The corresponding block extension of the Christoffel-Darboux theory is derived. De-formations of the quasi-definite matrix measure leading to integrable systems of Toda type are studied. The integrable theory is given in this matrix scenario; wave and adjoint wave functions, Lax and Zakharov-Shabat equations, bilinear equa-tions and discrete flows-connected with Darboux transformations. We generalize the integrable flows of the Cafasso’s matrix extension of the Toeplitz lattice for the Verblunsky coefficients of Szegő polynomials. An analysis of the Miwa shifts allows for the finding of interesting connections between Christoffel-Darboux kernels and Miwa shifts of the matrix orthogonal Laurent polynomials
dc.description.sponsorship M.M. thanks economical support from the Spanish “Ministerio de Economía y Competitividad” research project MTM2012-36732-C03-01, Ortogonalidad y aproximación; teoría y aplicaciones.
dc.format.extent 69
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights © Elsevier 2014
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.subject.other Matrix orthogonal Laurent polynomials
dc.subject.other Borel-Gauss factorization
dc.subject.other Christoffel-Darboux kernels
dc.subject.other Toda type integrable hierarchies
dc.title Matrix orthogonal Laurent polynomials on the unit circle and Toda type integrable systems
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2012-36732-C03-01
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 396
dc.identifier.publicationlastpage 463
dc.identifier.publicationtitle Advances in Mathematics
dc.identifier.publicationvolume 264
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