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      The Askey-Wilson function transform

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          Abstract

          In this paper we present an explicit (rank one) function transform which contains several Jacobi-type function transforms and Hankel-type transforms as degenerate cases. The kernel of the transform, which is given explicitly in terms of basic hypergeometric series, thus generalizes the Jacobi function as well as the Bessel function. The kernel is named the Askey-Wilson function, since it provides an analytical continuation of the Askey-Wilson polynomial in its degree. In this paper we establish the \(L^2\)-theory of the Askey-Wilson function transform, and we explicitely determine its inversion formula.

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          Author and article information

          Journal
          10 April 2000
          Article
          math/0004053
          af6d2e2a-d814-4725-884f-546afd62c625
          History
          Custom metadata
          33D45, 44A20, 33D80, 44A60
          Intern. Math. Res. Notices 22 (2001), 1203-1227
          LaTeX2e file. 19 pages
          math.CA math.QA math.RT

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