The Askey-Wilson function transform
By Erik Koelink, Jasper V. Stokman. 2000
66 citations recorded by the source corpus.
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 explicitly determine its inversion formula.
Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/d464647722c92bed8f3fdb8f2da2406df4a9084f
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In Applied Mathematics
In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Koornwinder polynomials and affine Hecke algebras (2000, methodology): “es of the bi-orthogonality weight function. This method is also expected to be an important tool for obtaining a better understanding of q-analogues of the Cherednik-Opdam transform, see e.g. [7] and [13] for some preliminary considerations in the rank one setting. The results of this paper extend t”