16 citations · 18 across the 4 of their papers we have counts for
4 papers
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…
Matrix differential equations and scalar polynomials satisfying higher order recursions
Antonio J. Duran, F. Alberto Grünbaum
We show that any scalar differential operator with a family of polyno- mials as its common eigenfunctions leads canonically to a matrix differen- tial operator with the same proper…
The Darboux process and a noncommutative bispectral problem
F. Alberto Grünbaum
The Darboux process, also known by many other names, played a very important role in some extremely enjoyable joint work that Hans and I did 25 years ago. I revisit a version of th…
Discrete bispectral Darboux transformations from Jacobi operators
F. Alberto Grünbaum, Milen Yakimov
We construct families of bispectral difference operators of the form a(n)T + b(n) + c(n) T^{-1} where T is the shift operator. They are obtained as discrete Darboux transformations…