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)
We develop structural formulas satisfied by some families of orthogonal matrix polynomials of size 2 × 2 satisfying second order differential equations with polynomial coefficients. We consider here two one parametric families of weight matrices, namely Ha,1(t) = e −t 2 1 + |a| 2 t 2 at ¯ at 1 and Ha,2(t) = e −t 2 1 + |a| 2 t 4 at 2 ¯ at 2 1 , a ∈ C and t ∈(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)
In this paper we announce that a very large class of integral operators derived from bispectral algebras of rank 1 and 2 (parametrized by Lagrangian Grassmannians of infinitely large size) posses commuting differential operators. The examples of Landau, Pollak, Slepian, and Tracy, Widom, used in time-band limiting and random matrix theory arise as special(More)