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arXiv · 1612.07229

Generalized Sobolev orthogonal polynomials, matrix moment problems and integrable systems

Gerardo Ariznabarreta·Manuel Mañas·Piergiulio Tempesta
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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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Gerardo Ariznabarreta, Manuel Mañas, Piergiulio Tempesta. 2016-12-15. Generalized Sobolev orthogonal polynomials, matrix moment problems and integrable systems. https://arxiv.org/abs/1612.07229

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