41 citations · 42 across the 6 of their papers we have counts for
7 papers
Matrix Bispectrality and Noncommutative Algebras: beyond the prolate spheroidals
F. Alberto Grünbaum, Brian D. Vasquez, Jorge P. Zubelli
The bispectral problem is motivated by an effort to understand and extend a remarkable phenomenon in Fourier analysis on the real line: the operator of time-and-band limiting is an…
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…
An urn model for the Jacobi-Piñeiro polynomials
F. Alberto Grünbaum, Manuel D. de la Iglesia
The list of physically motivated urn models that can be solved in terms of classical orthogonal polynomials is very small. It includes a model proposed by D. Bernoulli and further…
Algebraic Heun operator and band-time limiting
F. Alberto Grünbaum, Luc Vinet, Alexei Zhedanov
We introduce the algebraic Heun operator associated to any bispectral pair of operators. We show that these operators are natural generalizations of the ordinary Heun operator. Thi…
A generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks
F. Alberto Grünbaum, Luis Velázquez
Recent work on recurrence in quantum walks has provided a representation of Schur functions in terms of unitary operators. We propose a generalization of Schur functions by extendi…
The prolate spheroidal phenomena and bispectrality
F. Alberto Grünbaum, Milen Yakimov
Landau, Pollak, Slepian, and Tracy, Widom discovered that certain integral operators with so called Bessel and Airy kernels possess commuting differential operators and found impor…