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Fuchsian bispectral operators

Authors
Journal
Bulletin des Sciences Mathématiques
0007-4497
Publisher
Elsevier
Publication Date
Volume
126
Issue
3
Identifiers
DOI: 10.1016/s0007-4497(02)01109-0
Disciplines
  • Mathematics

Abstract

Abstract The aim of this paper is to classify the bispectral operators of any rank with regular singular points (the infinite point is the most important one). We characterise them in several ways. Probably the most important result is that they are all Darboux transformations of powers of generalised Bessel operators (in the terminology of [4]). For this reason they can be effectively parametrised by the points of a certain (infinite) family of algebraic manifolds as pointed out in [4].

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