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The discrete version of the bispectral problem. (English) Zbl 0902.39006

Harnad, John (ed.) et al., The bispectral problem. Proceedings of the CRM workshop, Montréal, Canada, March 1997. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 14, 93-104 (1998).
Authors’ abstract: We consider a discrete version of the bispectral problem. In this case, the solution can be given in terms of the \(q\)-Racah polynomials of Askey-Wilson. We see that an analog of the Darboux transformation preserves bispectrality. We show that applying a “dressing” Darboux transformation has the same effect as adding a new mass at zero and we conjecture the appearance of analogs of Krall polynomials.
For the entire collection see [Zbl 0885.00050].

MSC:

39A12 Discrete version of topics in analysis
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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