5 papers
Reflective prolate-spheroidal operators and the adelic Grassmannian
W. Riley Casper, F. Alberto Grünbaum, Milen Yakimov +1
Beginning with the work of Landau, Pollak and Slepian in the 1960s on time-band limiting, commuting pairs of integral and differential operators have played a key role in signal pr…
Reflective prolate-spheroidal operators and the KP/KdV equations
W. Riley Casper, F. Alberto Grunbaum, Milen Yakimov +1
Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was…
The Symmetric Hypergeometric Matrix Differential Operators
W. Riley Casper
We obtain an explicit classification of all real hypergeometric Bochner pairs, ie. pairs consisting of a real hypergeometric different…
A New Spectral Clustering Algorithm
W. R. Casper, Balu Nadiga
We present a new clustering algorithm that is based on searching for natural gaps in the components of the lowest energy eigenvectors of the Laplacian of a graph. In comparing the…
A Connection Between Orthogonal Polynomials and Shear Instabilities in the Quasi-geostrophic Shallow Water Equations
William Casper
In this paper we demonstrate a connection between the roots of a certain sequence of orthogonal polynomials on the real line and the linear instability of a -directionally homog…