Generalized Sobolev orthogonal polynomials, matrix moment problems and integrable systems

2016/12/15 by Gerardo Ariznabarreta, Ariznabarreta, Gerardo, Manuel Mañas +3
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CA #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.1612.07229

52 pages

arxiv created 2016/12/15 · arxiv updated 2016/12/22

Abstract

We introduce a large class of Sobolev bi-orthogonal polynomial sequences arising from a LU-factorizable moment matrix and associated with a suitable measure matrix that characterizes the Sobolev bilinear form. A theory of deformations of Sobolev bilinear forms is also proposed. We consider both polynomial deformations and a class of transformations related to the action of linear operators on the entries of a given bilinear form. Transformation formulae among new and old polynomial sequences are determined. Finally, integrable hierarchies of evolution equations arising from the factorization of a time deformation of the moment matrix are presented.

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