Bispectral operators of prime order
Mathematical Physics
2009-11-07 v1 math.MP
Abstract
The aim of this paper is to solve the bispectral problem for bispectral operators whose order is a prime number. More precisely we give a complete list of such bispectral operators. We use systematically the operator approach and in particular - Dixmier ideas on the first Weyl algebra. When the order is 2 the main theorem is exactly the result of Duistermaat-Gr\"unbaum . On the other hand our proofs seem to be simpler.
Cite
@article{arxiv.math-ph/0206029,
title = {Bispectral operators of prime order},
author = {Emil Horozov},
journal= {arXiv preprint arXiv:math-ph/0206029},
year = {2009}
}
Comments
25 pages, to appear in CMP