Publication: Matrix orthogonal Laurent polynomials on the unit circle and Toda type integrable systems
Loading...
Identifiers
Publication date
2014-10-20
Defense date
Authors
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Impact
Export
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
Description
Keywords
Matrix orthogonal Laurent polynomials, Borel-Gauss factorization, Christoffel-Darboux kernels, Toda type integrable hierarchies
Bibliographic citation
Advances in Mathematics, 2014, v. 264, pp. 396-463