F. Alberto Grünbaum

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Some families of orthogonal matrix polynomials satisfying second order differential equations with coefficients independent of n have recently been introduced (see [DG1]). An important difference with the scalar classical families of Jacobi, Laguerre and Hermite, is that these matrix families do not satisfy scalar type Rodrigues' formulas of the type (Φ n(More)
The main purpose of this paper is to compute all irreducible spherical functions on G = SU(3) of arbitrary type δ ∈ ˆ K, where K = S(U(2) × U(1)) ≃ U(2). This is accomplished by associating to a spherical function Φ on G a matrix valued function H on the complex projective plane P2(C) = G/K. It is well known that there is a fruitful connection between the(More)
In the case of the heat equation ut = uxx + V u on the real line there are some remarkable potentials V for which the asymptotic expansion of the fundamental solution becomes a finite sum and gives an exact formula. We show that a similar phenomenon holds when one replaces the real line by the integers. In this case the second derivative is replaced by the(More)
A method for reconstructing images from projections is described. The unique aspect of the procedure is that the reconstruction of the internal structure can be carried out for objects that diffuse the incident radiation. The method may be used with photons, phonons, neutrons, and many other kinds of radiation. The procedure has applications to medical(More)