Gómez-Ullate Oteiza, David

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First Name
Last Name
Gómez-Ullate Oteiza
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Físicas
Física Teórica
Matemática Aplicada
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  • Publication
    Exceptional Legendre polynomials and confluent Darboux transformations
    (Natl Acad Sci Ukraine, Inst Math, 2021) Garcia Ferrero, María Ángeles; Gómez-Ullate Oteiza, David; Milson, Robert
    Exceptional 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.