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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… (More)

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… (More)

Abstract
We develop structural formulas
satisfied by some families of
orthogonal matrix polynomials of size $2\times 2$ satisfying
second-order differential equations with polynomial coefficients. We… (More)

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… (More)

Abstract For every value of the parameters α , β >−1 we find a matrix valued weight whose orthogonal polynomials satisfy an explicit differential equation of Jacobi type.

The three-dimensional configuration of crystallized structures is obtained by reading off partial information about the Fourier transform of such structures from diffraction data obtained with an… (More)

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… (More)

The classical (scalar-valued) theory of spherical functions, put forward by Cartan and others, unifies under one roof a number of examples that were very well-known before the theory was formulated.… (More)

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… (More)