126 citations · 447 across the 20 of their papers we have counts for
9 papers · 1 filter
Ad-conditions for higher-order recurrences: Dunkl and matrix-valued settings
I. Bono Parisi, F. A. Grünbaum, I. Zurrián
The ad-conditions of Duistermaat and Grünbaum characterize bispectrality for a pair of differential operators. M.~Reach observed that a sequence of functions which is simultaneousl…
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…
A new commutativity property of exceptional orthogonal polynomials
M. M. Castro, F. A. Grünbaum
We exhibit three examples showing that the "time-and-band limiting" commutative property found and exploited by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's, and…
Bispectrality and Time-Band-Limiting: Matrix valued polynomials
F. Alberto Grünbaum, Inés Pacharoni, Ignacio N. Zurrián
The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one al…
A further look at time-and-band limiting for matrix orthogonal polynomials
M. Castro, F. A. Grünbaum, I. Pacharoni +1
We extend to a situation involving matrix valued orthogonal polynomials a scalar result that originates in work of Claude Shannon and a ground-breaking series of papers by D. Slepi…
The CMV bispectral problem
F. A. Grünbaum, L. Velázquez
A classical result due to Bochner classifies the orthogonal polynomials on the real line which are common eigenfunctions of a second order linear differential operator. We settle a…
A quantum dynamical approach to matrix Khrushchev's formulas
C. Cedzich, F. A. Grünbaum, L. Velázquez +2
Khrushchev's formula is the cornerstone of the so called Khrushchev theory, a body of results which has revolutionized the theory of orthogonal polynomials on the unit circle. This…
On a Family of 2-Variable Orthogonal Krawtchouk Polynomials
F. Alberto Grünbaum, Mizan Rahman
We give a hypergeometric proof involving a family of 2-variable Krawtchouk polynomials that were obtained earlier by Hoare and Rahman [SIGMA 4 (2008), 089, 18 pages] as a limit of…
Heat kernel expansions on the integers
F. Alberto Grunbaum, Plamen Iliev
In the case of the heat equation on the real line there are some remarkable potentials for which the asymptotic expansion of the fundamental solution becomes a…