TL;DR
This paper classifies all bispectral operators of prime order using algebraic methods, extending known results for order 2 and providing a comprehensive list for higher prime orders.
Contribution
It offers a complete classification of bispectral operators of prime order, utilizing the operator approach and Weyl algebra techniques, simplifying previous proofs.
Findings
Complete list of bispectral operators of prime order
Extension of Duistermaat-Grünbaum result for order 2
Simplified proofs using Weyl algebra methods
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.
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