A Bochner type classification theorem for exceptional orthogonal polynomials
Classical Analysis and ODEs
2017-02-07 v2
Abstract
It was recently conjectured that every system of exceptional orthogonal polynomials is related to classical orthogonal polynomials by a sequence of Darboux transformations. In this paper we prove this conjecture, which paves the road to a complete classification of all exceptional orthogonal polynomials. In some sense, this paper can be regarded as the extension of Bochner's result for classical orthogonal polynomials to the exceptional class. As a supplementary result, we derive a canonical form for exceptional operators based on a bilinear formalism, and prove that every exceptional operator has trivial monodromy at all primary poles.
Cite
@article{arxiv.1603.04358,
title = {A Bochner type classification theorem for exceptional orthogonal polynomials},
author = {M. Ángeles García-Ferrero and David Gómez-Ullate and Robert Milson},
journal= {arXiv preprint arXiv:1603.04358},
year = {2017}
}
Comments
a number of minor mistakes have been corrected. some proofs have been streamlined and simplified