136 citations · 166 across the 13 of their papers we have counts for
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Matrix valued discrete-continuous functions with the prolate spheroidal property and bispectrality
W. Riley Casper, F. Alberto Grunbaum, Milen Yakimov +1
Classical prolate spheroidal functions play an important role in the study of time-band limiting, scaling limits of random matrices, and the distribution of the zeros of the Rieman…
Algebras of commuting differential operators for integral kernels of Airy type
W. Riley Casper, F. Alberto Grunbaum, Milen Yakimov +1
Differential operators commuting with integral operators were discovered in the work of C. Tracy and H. Widom [37, 38] and used to derive asymptotic expansions of the Fredholm dete…
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…
Integral operators, bispectrality and growth of Fourier algebras
W. Riley Casper, Milen T. Yakimov
In the mid 80's it was conjectured that every bispectral meromorphic function gives rise to an integral operator which possesses a commuting differential operat…
Elementary Examples of Solutions to Bochner's Problem for Matrix Differential Operators
William Casper
In this paper, we demonstrate an elementary method for constructing new solutions to Bochner's problem for matrix differential operators from known solutions. We then describe a la…