In search of higher Bochner theorem
Mathematical Physics
2024-08-08 v2 High Energy Physics - Theory
Classical Analysis and ODEs
math.MP
Abstract
We initiate the study of a natural generalisation of the classical Bochner-Krall problem asking which linear ordinary differential operators possess sequences of eigenpolynomials satisfying linear recurrence relations of finite length; the classical case corresponds to the 3-term recurrence relations with real coefficients subject to some extra restrictions. We formulate a general conjecture and prove it in the first non-trivial case of operators of order 3.
Keywords
Cite
@article{arxiv.1807.01558,
title = {In search of higher Bochner theorem},
author = {Emil Horozov and Boris Shapiro and Milos Tater},
journal= {arXiv preprint arXiv:1807.01558},
year = {2024}
}
Comments
Substantially revised and shortened version. Content of Sections 4 and 5 simplified. Computational formulas in Appendix ii corrected. To appear in JAT