English

Hessenberg-Sobolev Matrices and Favard type theorems

Classical Analysis and ODEs 2022-11-11 v3 Complex Variables

Abstract

We study the relation between certain non-degenerate lower Hessenberg infinite matrices G\mathcal{G} and the existence of sequences of orthogonal polynomials with respect to Sobolev inner products. In other words, we extend the well-known Favard theorem for Sobolev orthogonality. We characterize the structure of the matrix G\mathcal{G} and the associated matrix of formal moments MG\mathcal{M}_{\mathcal{G}} in terms of certain matrix operators.

Keywords

Cite

@article{arxiv.2206.05612,
  title  = {Hessenberg-Sobolev Matrices and Favard type theorems},
  author = {Hector Pijeira-Cabrera and Laura Decalo-Salgado and Ignacio Perez-Yzquierdo},
  journal= {arXiv preprint arXiv:2206.05612},
  year   = {2022}
}
R2 v1 2026-06-24T11:47:42.592Z