%0 Journal Article
%A García Ferrero, María Ángeles
%A Gómez-Ullate Oteiza, David
%A Milson, Robert
%T A Bochner type characterization theorem for exceptional orthogonal polynomials
%D 2019
%@ 0022-247X
%U https://hdl.handle.net/20.500.14352/13153
%X It was recently conjectured that every system of exceptional orthogonal polynomials is related to a classical orthogonal polynomial system by a sequence of Darboux transformations. In this paper we prove this conjecture, which paves the road to a complete classification of all exceptional orthogonal polynomials. In some sense, this paper can be regarded as the extension of Bochner's result for classical orthogonal polynomials to the exceptional class. As a supplementary result, we derive a canonical form for exceptional operators based on a bilinear formalism, and prove that every exceptional operator has trivial monodromy at all primary poles.
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