126 citations · 447 across the 20 of their papers we have counts for
21 papers
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…
Time and band limiting for exceptional polynomials
M. M. Castro, F. A. Grünbaum, I. Zurrián
The "time-and-band limiting" commutative property was found and exploited by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's, and independently by M. Mehta and later…
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…
Quantum walks: Schur functions meet symmetry protected topological phases
C. Cedzich, T. Geib, F. A. Grünbaum +3
This paper uncovers and exploits a link between a central object in harmonic analysis, the so-called Schur functions, and the very hot topic of symmetry protected topological phase…
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 topological classification of one-dimensional symmetric quantum walks
C. Cedzich, T. Geib, F. A. Grünbaum +4
We give a topological classification of quantum walks on an infinite 1D lattice, which obey one of the discrete symmetry groups of the tenfold way, have a gap around some eigenvalu…
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…
Time and band limiting for matrix valued functions: an integral and a commuting differential operator
F. Alberto Grünbaum, Inés Pacharoni, Ignacio Nahuel Zurrián
The problem of recovering a signal of finite duration from a piece of its Fourier transform was solved at Bell Labs in the 's, by exploiting a "miracle": a certain naturally…
Tridiagonalization and the Heun equation
F. Alberto Grünbaum, Luc Vinet, Alexei Zhedanov
It is shown that the tridiagonalization of the hypergeometric operator yields the generic Heun operator . The algebra generated by the operators and is quadr…
Bulk-edge correspondence of one-dimensional quantum walks
C. Cedzich, F. A. Grünbaum, C. Stahl +3
We outline a theory of symmetry protected topological phases of one-dimensional quantum walks. We assume spectral gaps around the symmetry-distinguished points +1 and -1, in which…
Time and Band Limiting for Matrix Valued Functions, an Example
F. Alberto Grünbaum, Inés Pacharoni, Ignacio Nahuel Zurrián
The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importanc…
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…
A limit theorem for a 3-period time-dependent quantum walk
F. Alberto Grünbaum, Takuya Machida
We consider a discrete-time 2-state quantum walk on the line. The state of the quantum walker evolves according to a rule which is determined by a coin-flip operator and a position…
Birth and death processes and quantum spin chains
Alberto F. Grünbaum, Luc Vinet, Alexei Zhedanov
This papers underscores the intimate connection between the quantum walks generated by certain spin chain Hamiltonians and classical birth and death processes. It is observed that…
Recurrence for discrete time unitary evolutions
F. A. Grünbaum, L. Velázquez, A. H. Werner +1
We consider quantum dynamical systems specified by a unitary operator U and an initial state vector ϕ. In each step the unitary is followed by a projective measurement checking whe…
The Quantum Walk of F. Riesz
F. A. Grunbaum, L. Velazquez
We exhibit a way to associate a quantum walk (QW) on the non-negative integers to any probability measure on the unit circle. This forces us to consider one step transitions that a…
A System of Multivariable Krawtchouk Polynomials and a Probabilistic Application
F. Alberto Grünbaum, Mizan Rahman
The one variable Krawtchouk polynomials, a special case of the function did appear in the spectral representation of the transition kernel for a Markov chain studied a long…
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…