178 citations · 609 across the 31 of their papers we have counts for
32 papers
-step rational extensions of the trigonometric Darboux-Pöschl-Teller potential based on para-Jacobi polynomials
Yves Grandati, Christiane Quesne
A previous construction of regular rational extensions of the trigonometric Darboux-Pöschl-Teller potential, obtained by one-step Darboux transformations using seed functions assoc…
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…
Complete classification of rational solutions of -Painlevé systems
David Gómez-Ullate, Yves Grandati, Robert Milson
We provide a complete classification and an explicit representation of rational solutions to the fourth Painlevé equation PIV and its higher order generalizations known as the $A_{…
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…