Strictly nilpotent elements and bispectral operators in the Weyl algebra

Details Strictly nilpotent elements and bispectral operators in the Weyl algebra Strictly nilpotent elements and bispectral operators in the Weyl algebra

2002-06-18

arxiv.org/abs/math-ph/0206030v1

Physics

Mathematical Physics

11 pages, to appear in Bull. Sci. Math

Scientific paper

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).

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