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- F. A. GRÜNBAUM
- 2008

The main purpose of this paper is to compute all irreducible spherical functions on G = SU(3) of arbitrary type δ ∈ K̂, 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)

- F. Alberto Grünbaum, Manuel D. de la Iglesia
- Experimental Mathematics
- 2007

The theory of matrix valued orthogonal polynomials (MVOP) was introduced by M. G. Krein in 1949. Systematically studied in the last 15 years.

Abstract. 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… (More)

- Antonio J. Durán Guardeño, F. Alberto Grünbaum
- Journal of Approximation Theory
- 2007

- F. A. GRÜNBAUM
- 2004

The classical (scalar valued) theory of spherical functions (put forward by Cartan and others after him) allows one to unify under one roof a number of examples that were very well known before the theory was formulated. These examples include many special functions like Jacobi polynomials, Bessel functions, Laguerre polynomials, Hermite polynomials,… (More)

- María José Cantero, F. Alberto Grünbaum, Leandro Moral, Luis Velázquez
- Quantum Information Processing
- 2012

- F. A. GRÜNBAUM
- 2008

The main purpose of this paper is to compute all irreducible spherical functions on G = SL(2,C) of arbitrary type δ ∈ K̂, where K = SU(2). This is accomplished by associating to a spherical function Φ on G a matrix valued function H on the three dimensional hyperbolic space H = G/K. The entries of H are solutions of two coupled systems of ordinary… (More)

I revisit the so called “bispectral problem” introduced in a joint paper with Hans Duistermaat a long time ago, allowing now for the differential operators to have matrix coefficients and for the eigenfunctions, and one of the eigenvalues, to be matrix valued too. In the last example we go beyond this and allow both eigenvalues to be matrix valued.

- J R Singer, F A Grünbaum, P Kohn, J P Zubelli
- Science
- 1990

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)

- Elisenda Miró, Federico Grünbaum, +4 authors Ferran Navarro
- Microbial drug resistance
- 2013

A total of 788 clinical Enterobacteriaceae were collected to describe the aminoglycoside-modifying genes (AME genes) and to characterize the plasmids that carry these genes. Among the 788 strains collected, 330 (41.8%) were aminoglycoside-resistant: 264 Escherichia coli (80%), 33 Proteus mirabilis (10%), 10 Klebsiella pneumoniae (3%), six K. oxytoca (1.8%),… (More)