13 citations · 13 across the 6 of their papers we have counts for
9 papers
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…
Rational solutions of Painleve systems
David Gomez-Ullate, Yves Grandati, Robert Milson
Although the solutions of Painlevé equations are transcendental in the sense that they cannot be expressed in terms of known elementary functions, there do exist rational solutions…
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…
Ladder operators and rational extensions
David Gomez-Ullate, Yves Grandati, Zoe McIntyre +1
This note presents the classification of ladder operators corresponding to the class of rational extensions of the harmonic oscillator. We show that it is natural to endow the clas…
Rational solutions of dressing chains and higher order Painleve equations
D. Gomez-Ullate, Y. Grandati, S. Lombardo +1
We present a new approach to determine the rational solutions of the higher order Painleve equations associated to periodic dressing chain systems. We obtain new sets of solutions,…