García Ferrero, María ÁngelesGómez-Ullate Oteiza, DavidMilson, Robert2023-06-172023-06-172019-04-010022-247X10.1016/j.jmaa.2018.11.042https://hdl.handle.net/20.500.14352/13153©2018 Elsevier Inc. M.A.G.F. acknowledges the financial support of the Spanish MINECO through a Severo Ochoa FPI scholarship. The work of M.A.G.F. is supported in part by the ERC Starting Grant 633152 and the ICMAT-Severo Ochoa project SEV-2015-0554. The research of D.G.U. has been supported in part by Spanish MINECO-FEDER Grants MTM2012-31714 and MTM2015-65888-C4-3 and by the ICMAT-Severo Ochoa project SEV-2015-0554. The research of the third author (RM) was supported in part by NSERC grant RGPIN-228057-2009. D.G.U. would like to thank Dalhousie University for their hospitality during his visit in the Spring semester of 2014 where many of the results in this paper were obtained.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.engAtribución-NoComercial-SinDerivadas 3.0 Españajournal articlehttp://dx.doi.org/10.1016/j.jmaa.2018.11.042https://www.sciencedirect.comopen access51-73Shape invariant potentialsScattering-amplitudeDarboux transformationsHermiteZerosExtensionsFamiliesCharlierMeixnerOrthogonal polynomialsSturm-Liouville problemsTrivial monodromyFísica-Modelos matemáticosFísica matemática