17 citations · 57 across the 14 of their papers we have counts for
6 papers · 1 filter
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_{…
Constructing Coherent States for the Rational Extensions of the Harmonic Oscillator Potential
Zoé McIntyre, Robert Milson
Using the formalism of Maya diagrams and ladder operators, we describe the algebra of annihilating operators for the class of rational extensions of the harmonic oscillators. This…
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…
Exceptional Legendre Polynomials and Confluent Darboux Transformations
María Ángeles García-Ferrero, David Gómez-Ullate, Robert Milson
Exceptional orthogonal polynomials are families of orthogonal polynomials that arise as solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of…
The Adelic Grassmannian and Exceptional Hermite Polynomials
Alex Kasman, Robert Milson
It is shown that when dependence on the second flow of the KP hierarchy is added, the resulting semi-stationary wave function of certain points in George Wilson's adelic Grassmanni…