Person: Gómez-Ullate Oteiza, David
Universidad Complutense de Madrid
Faculty / Institute
Now showing 1 - 2 of 2
PublicationExceptional Legendre polynomials and confluent Darboux transformations(Natl Acad Sci Ukraine, Inst Math, 2021) Garcia Ferrero, María Ángeles; Gómez-Ullate Oteiza, David; Milson, RobertExceptional orthogonal polynomials are families of orthogonal polynomials that arise as solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of Hermite, Laguerre, and Jacobi polynomials by allowing for polynomial sequences that miss a finite number of "exceptional" degrees. In this paper we introduce a new construction of multi-parameter exceptional Legendre polynomials by considering the isospectral deformation of the classical Legendre operator. Using confluent Darboux transformations and a technique from inverse scattering theory, we obtain a fully explicit description of the operators and polynomials in question. The main novelty of the paper is the novel construction that allows for exceptional polynomial families with an arbitrary number of real parameters. PublicationCorrigendum on the proof of completeness for exceptional Hermite polynomials.(Academic Press Inc Elsevier Science, 2020-05) Gómez-Ullate Oteiza, David; Grandati, Yves; Milson, RobertExceptional orthogonal polynomials are complete families of orthogonal polynomials that arise as eigenfunctions of a Sturm-Liouville problem. Antonio Duran discovered a gap in the original proof of completeness for exceptional Hermite polynomials, that has propagated to analogous results for other exceptional families In this paper we provide an alternative proof that follows essentially the same arguments, but provides a direct proof of the key lemma on which the completeness proof is based. This direct proof makes use of the theory of trivial monodromy potentials developed by Duistermaat and Grtinbaum and Oblomkov. (C) 2019 Published by Elsevier Inc.