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

Ariznabarreta, Gerardo; Mañas, Manuel

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

dc.affiliation.dpto	UC3M. Departamento de Matemáticas	es
dc.affiliation.grupoinv	UC3M. Grupo de Investigación: Análisis Aplicado	es
dc.contributor.author	Ariznabarreta, Gerardo
dc.contributor.author	Mañas, Manuel
dc.date.accessioned	2016-07-20T09:48:19Z
dc.date.available	2016-11-01T23:00:09Z
dc.date.issued	2014-10-20
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	en
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.	es
dc.format.extent	69
dc.format.mimetype	application/pdf
dc.identifier.bibliographicCitation	Advances in Mathematics, 2014, v. 264, pp. 396-463	en
dc.identifier.publicationfirstpage	396
dc.identifier.publicationlastpage	463
dc.identifier.publicationtitle	Advances in Mathematics	en
dc.identifier.publicationvolume	264
dc.identifier.uri	https://hdl.handle.net/10016/23388
dc.language.iso	eng
dc.publisher	Elsevier	en
dc.relation.projectID	Gobierno de España. MTM2012-36732-C03-01	es
dc.relation.publisherversion	http://dx.doi.org/10.1016/j.aim.2014.06.019
dc.rights	© Elsevier 2014	en
dc.rights	Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.accessRights	open access
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.eciencia	Matemáticas	es
dc.subject.other	Matrix orthogonal Laurent polynomials	en
dc.subject.other	Borel-Gauss factorization	en
dc.subject.other	Christoffel-Darboux kernels	en
dc.subject.other	Toda type integrable hierarchies	en
dc.title	Matrix orthogonal Laurent polynomials on the unit circle and Toda type integrable systems	en
dc.type	research article	*
dc.type.hasVersion	AM	*
dspace.entity.type	Publication