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 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 and the associated matrix of formal moments in terms of certain matrix operators.
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}
}