136 citations · 166 across the 13 of their papers we have counts for
15 papers
The Pascal Matrix, Commuting Tridiagonal Operators and Fourier Algebras
W. Riley Casper, Ignacio Zurrian
We consider the (symmetric) Pascal matrix, in its finite and infinite versions, and prove the existence of symmetric tridiagonal matrices commuting with it by giving explicit expre…
The restricted discrete Fourier transform
W. Riley Casper, Milen Yakimov
We investigate the restriction of the discrete Fourier transform to the space of functions with…
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…
A Burchnall-Chaundy-Krichever Theory for Fractional Differential Operators
W. Riley Casper, Emil Horozov, Plamen Iliev +1
Fractional differential (and difference) operators play a role in a number of diverse settings: integrable systems, mirror symmetry, Hurwitz numbers, the Bethe ansatz equations. We…
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…