349 citations · 1.5k across the 35 of their papers we have counts for
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Classification of exceptional Jacobi polynomials
Maria Angeles Garcia-Ferrero, David Gomez-Ullate, Robert Milson
We provide a full classification scheme for exceptional Jacobi operators and polynomials. The classification contains six degeneracy classes according to whether or a…
Exceptional Gegenbauer polynomials via isospectral deformation
María~Ángeles García-Ferrero, David Gómez-Ullate, Robert Milson +1
We show a method to construct isospectral deformations of classical orthogonal polynomials. The construction is based on confluent Darboux transformations, and it allows to constru…
Spectral Theory of Exceptional Hermite Polynomials
David Gomez-Ullate, Yves Grandati, Robert Milson
In this paper we revisit exceptional Hermite polynomials from the point of view of spectral theory, following the work initiated by Lance Littlejohn. Adapting a result of Deift, we…
Corrigendum on the proof of completeness for exceptional Hermite polynomials
David Gomez-Ullate, Yves Grandati, Robert Milson
Exceptional orthogonal polynomials are complete families of orthogonal polynomials that arise as eigenfunctions of a Sturm-Liouville problem. Antonio Durán discovered a gap in the…
Shape invariance and equivalence relations for pseudowronskians of Laguerre and Jacobi polynomials
David Gomez-Ullate, Yves Grandati, Robert Milson
In a previous paper we derived equivalence relations for pseudo-Wronskian determinants of Hermite polynomials. In this paper we obtain the analogous result for Laguerre and Jacobi…
Durfee rectangles and pseudo-Wronskian equivalences for Hermite polynomials
David Gomez-Ullate, Yves Grandati, Robert Milson
We study an equivalence class of iterated rational Darboux transformations applied on the harmonic oscillator, showing that many choices of state adding and state deleting transfor…
Recurrence Relations for Exceptional Hermite Polynomials
D. Gomez-Ullate, A. Kasman, A. B. J. Kuijlaars +1
The bispectral anti-isomorphism is applied to differential operators involving elements of the stabilizer ring to produce explicit formulas for all difference operators having any…