Strictly nilpotent elements and bispectral operators in the Weyl algebra
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
In this paper we give another characterization of the strictly nilpotent elements in the Weyl algebra, which (apart from the polynomials) turn out to be all bispectral operators with polynomial coefficients. This also allows to reformulate in terms of bispectral operators the famous conjecture, that all the endomorphisms of the Weyl algebra are automorphisms (Dixmier, Kirillov, etc).
Keywords
Cite
@article{arxiv.math-ph/0206030,
title = {Strictly nilpotent elements and bispectral operators in the Weyl algebra},
author = {Emil Horozov},
journal= {arXiv preprint arXiv:math-ph/0206030},
year = {2007}
}
Comments
11 pages, to appear in Bull. Sci. Math