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Differential equations in the spectral parameter
- J. Duistermaat, F. Grünbaum
- Mathematics
- 1 June 1986
We determine all the potentialsV(x) for the Schrödinger equation (−∂x2+V(x))∅=k2∅ such that some family of eigenfunctions ∅ satisfies a differential equation in the spectral parameterk of the…
Orthogonal matrix polynomials satisfying second-order differential equations
- A. J. Durán, F. Grünbaum
- Mathematics
- 2004
We develop a general method that allows us to introduce families of orthogonal matrix polynomials of size N × N satisfying second-order differential equations. The presence of this extra property…
Recurrence for Discrete Time Unitary Evolutions
- F. Grünbaum, L. Velázquez, A. H. Werner, R. Werner
- Mathematics
- 17 February 2012
We consider quantum dynamical systems specified by a unitary operator U and an initial state vector $${\phi}$$. In each step the unitary is followed by a projective measurement checking whether the…
Matrix‐valued Szegő polynomials and quantum random walks
- M. J. Cantero, L. Moral, F. Grünbaum, L. Velázquez
- Mathematics
- 15 January 2009
We consider quantum random walks (QRW) on the integers, a subject that has been considered in the last few years in the framework of quantum computation.
The Algebra of Differential Operators Associated to a Weight Matrix
- F. Grünbaum, J. Tirao
- Mathematics
- 27 June 2007
Abstract.Given a weight matrix W(x) of size N on the real line one constructs a sequence of matrix valued orthogonal polynomials, {Pn}n≥0. We study the algebra
$${\mathcal{D}}(W)$$
of differential…
The eigenvectors of the discrete Fourier transform: A version of the Hermite functions
- F. Grünbaum
- Mathematics
- 1 August 1982
Dromions and a boundary value problem for the Davey-Stewartson 1 equation
- F. Grünbaum
- Mathematics
- 1 August 1990
Eigenvectors of a Toeplitz Matrix: Discrete Version of the Prolate Spheroidal Wave Functions
- F. Grünbaum
- Computer Science
- 1 June 1981
The discrete Fourier transform leads one, in a natural way, to consider the extent to which a function in $Z_N $ and its transform can both be sharply concentrated. This requires the study of a…
Differential Operators Commuting with Finite Convolution Integral Operators: Some Nonabelian Examples
- F. Grünbaum, L. Longhi, M. Perlstadt
- Mathematics
- 1 October 1982
Slepian, Landau and Pollak found that a certain finite convolution integral operator on the real line commutes with a much simpler second order differential operator. This opens the way to a detailed…
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