Generalized Sobolev orthogonal polynomials, matrix moment problems and integrable systems

Gerardo Ariznabarreta; Manuel Mañas; Piergiulio Tempesta

Generalized Sobolev orthogonal polynomials, matrix moment problems and integrable systems

Classical Analysis and ODEs 2016-12-22 v1 Mathematical Physics math.MP Exactly Solvable and Integrable Systems

Authors: Gerardo Ariznabarreta , Manuel Mañas , Piergiulio Tempesta

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.

Keywords

orthogonal polynomials sobolev spaces sobolev regularity of partial differential equations

Cite

@article{arxiv.1612.07229,
  title  = {Generalized Sobolev orthogonal polynomials, matrix moment problems and integrable systems},
  author = {Gerardo Ariznabarreta and Manuel Mañas and Piergiulio Tempesta},
  journal= {arXiv preprint arXiv:1612.07229},
  year   = {2016}
}

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52 pages

Generalized Sobolev orthogonal polynomials, matrix moment problems and integrable systems

Abstract

Keywords

Cite

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