D
David Gómez-Ullate
Researcher at University of Cádiz
Publications - 109
Citations - 3103
David Gómez-Ullate is an academic researcher from University of Cádiz. The author has contributed to research in topics: Orthogonal polynomials & Hermite polynomials. The author has an hindex of 27, co-authored 103 publications receiving 2902 citations. Previous affiliations of David Gómez-Ullate include Université de Montréal & Centre de Recherches Mathématiques.
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An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
TL;DR: In this article, two infinite sequences of polynomial eigenfunctions of a Sturm-Liouville problem are presented, and they are shown to be orthogonal with respect to a positive definite inner product defined over the compact interval [ − 1, 1 ] or the half-line [ 0, ∞ ), respectively.
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An extension of Bochner's problem: Exceptional invariant subspaces
TL;DR: The main theorem of the paper provides a characterization of all such differential operators and polynomial sequences based on the classification of codimension one exceptional subspaces under projective transformations.
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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
TL;DR: In this article, it was shown that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the harmonic oscillators.
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Exceptional orthogonal polynomials and the Darboux transformation
TL;DR: In this paper, the authors adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems and characterize the Xm Laguerre polynomials in terms of an isospectral Darbouque transformation.
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Two-step Darboux transformations and exceptional Laguerre polynomials
TL;DR: In this article, a 2-step algebraic Darboux transformation of the classical Laguerre polynomials is presented, which gives rise to a new orthogonal polynomial system indexed by two integer parameters.