Bispectral operators of prime order

Details Bispectral operators of prime order Bispectral operators of prime order

2002-06-18

arxiv.org/abs/math-ph/0206029v1

Physics

Mathematical Physics

25 pages, to appear in CMP

Scientific paper

10.1007/s00220-002-0717-0

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.

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