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.
The author was supported in part by NSF Grant DMS-0603901.
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Communicated by L. Rodman.
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Grünbaum, F.A. (2010). A Spectral Weight Matrix for a Discrete Version of Walsh’s Spider. In: Topics in Operator Theory. Operator Theory: Advances and Applications, vol 202. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0158-0_12
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DOI: https://doi.org/10.1007/978-3-0346-0158-0_12
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