Banded matrices and their orthogonality
Classical Analysis and ODEs
2023-07-18 v1
Abstract
Banded bounded matrices, which represent non normal operators, of oscillatory type that admit a positive bidiagonal factorization are considered. To motivate the relevance of the oscillatory character the Favard theorem for Jacobi matrices is revisited and it is shown that after an adequate shift of the Jacobi matrix one gets an oscillatory matrix. In this work we present a spectral theorem for this type of operators and show how the theory of multiple orthogonal polynomials apply.
Cite
@article{arxiv.2307.08081,
title = {Banded matrices and their orthogonality},
author = {Amílcar Branquinho and Ana Foulquié-Moreno and Manuel Mañas},
journal= {arXiv preprint arXiv:2307.08081},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2203.13578