On polynomial solutions of certain finite order ordinary differential equations
Functional Analysis
2023-09-20 v1
Abstract
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well as the corresponding eigenvalues. Also, some linear transformations are applied to sequences of eigenfunctions and a necessary condition for this to be a sequence of eigenfunctions of a new differential operator is obtained. These results are applied to the particular case of classical Hermite polynomials.
Keywords
Cite
@article{arxiv.2309.10059,
title = {On polynomial solutions of certain finite order ordinary differential equations},
author = {L. M. Anguas and D. Barrios Rolanía},
journal= {arXiv preprint arXiv:2309.10059},
year = {2023}
}