A Spectral Weight Matrix for a Discrete Version of Walsh’s Spider

  • F. Alberto Grünbaum
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 202)

Abstract

We consider a discrete space version of Walsh’s spider, see [W] as well as [ES] and its references. This process can be seen as an instance of a quasi-birth-and-death process, a class of random walks for which the classical theory of Karlin and McGregor can be nicely adapted as in [DRSZ], [G1, G2] and [GdI]. We give here a simple expression for a family of weight matrices that make the corresponding matrix-valued orthogonal polynomials orthogonal to each other.

Keywords

Matrix-valued orthogonal polynomials Karlin-McGregor representation 

Mathematics Subject Classification (2000)

33C45 22E45 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • F. Alberto Grünbaum
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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