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Differential equations in the spectral parameter
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
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
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
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
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
Eigenvectors of a Toeplitz Matrix: Discrete Version of the Prolate Spheroidal Wave Functions
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
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