Strictly nilpotent elements and bispectral operators in the Weyl algebra |
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Authors: | E. Horozov |
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Affiliation: | Department of Mathematics and Informatics, Sofia University, 5 J. Bourchier Blvd., Sofia 1126, Bulgaria |
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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). |
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Keywords: | Weyl algebra Bispectral operators Automorphism group Strictly nilpotent elements |
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