Перегляд за автором "Grünbaum, F.A."

Сортувати за: Порядок: Результатів:

  • A System of Multivariable Krawtchouk Polynomials and a Probabilistic Application 
    Grünbaum, F.A.; Rahman, M. (Symmetry, Integrability and Geometry: Methods and Applications, 2011)
    The one variable Krawtchouk polynomials, a special case of the ₂F₁ function did appear in the spectral representation of the transition kernel for a Markov chain studied a long time ago by M. Hoare and M. Rahman. A ...
  • On a Family of 2-Variable Orthogonal Krawtchouk Polynomials 
    Grünbaum, F.A.; Rahman, M. (Symmetry, Integrability and Geometry: Methods and Applications, 2010)
    We give a hypergeometric proof involving a family of 2-variable Krawtchouk polynomials that were obtained earlier by Hoare and Rahman [SIGMA 4 (2008), 089, 18 pages] as a limit of the 9−j symbols of quantum angular momentum ...
  • On a Seminal Paper by Karlin and McGregor 
    Castro, M.M.; Grünbaum, F.A. (Symmetry, Integrability and Geometry: Methods and Applications, 2013)
    The use of spectral methods to study birth-and-death processes was pioneered by S. Karlin and J. McGregor. Their expression for the transition probabilities was made explicit by them in a few cases. Here we complete their ...
  • Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization 
    Grünbaum, F.A.; de la Iglesia, M.D.; Martínez-Finkelshtein, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2011)
    We give a Riemann-Hilbert approach to the theory of matrix orthogonal polynomials. We will focus on the algebraic aspects of the problem, obtaining difference and differential relations satisfied by the corresponding ...
  • Some Noncommutative Matrix Algebras Arising in the Bispectral Problem 
    Grünbaum, F.A. (Symmetry, Integrability and Geometry: Methods and Applications, 2014)
    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 ...
  • The Rahman Polynomials Are Bispectral 
    Grünbaum, F.A. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
    In a very recent paper, M. Rahman introduced a remarkable family of polynomials in two variables as the eigenfunctions of the transition matrix for a nontrivial Markov chain due to M. Hoare and M. Rahman. I indicate here ...
  • Time and Band Limiting for Matrix Valued Functions, an Example 
    Grünbaum, F.A.; Pacharoni, I.; Zurrián, I.N. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importance to work of Claude Shannon in laying the ...