Observatorio de I+D+i UPM

Descripción
n this paper, Geronimus?Uvarov perturbations for matrix orthogonal polynomials on the real line are studied and then applied to the analysis of non-Abelian integrable hierarchies. The orthogonality is understood in full generality, ie in terms of a nondegenerate continuous sesquilinear form, determined by a quasidefinite matrix of bivariate generalized functions with a well-defined support. We derive Christoffel-type formulas that give the perturbed matrix biorthogonal polynomials and their norms in terms of the original ones. The keystone for this finding is the Gauss?Borel factorization of the Gram matrix. Geronimus?Uvarov transformations are considered in the context of the 2D non-Abelian Toda lattice and noncommutative KP hierarchies. The interplay between transformations and integrable flows is discussed. Miwa shifts, ?-ratio matrix functions and Sato formulas are given
Internacional	Si
JCR del ISI	No
Título de la revista	Journal of Physics a: Mathematical And Theoretical
ISSN	1751-8113
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• Autor: Juan Carlos Garcia Ardila (UPM)
• Autor: Francisco Marcellán (UC3M)
• Autor: Manuel Enrique Mañas Baena (UCM)
• Autor: Gerardo Ariznabarreta (Universidad Complutense)

• Creador: Grupo de Investigación: Teoría de Aproximación Constructiva y Aplicaciones