The Askey-Wilson function transform

Details The Askey-Wilson function transform The Askey-Wilson function transform

2000-04-10

arxiv.org/abs/math/0004053v1

Intern. Math. Res. Notices 22 (2001), 1203-1227

Mathematics

Classical Analysis and ODEs

LaTeX2e file. 19 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The Askey-Wilson function transform does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Askey-Wilson function transform, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Askey-Wilson function transform will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-139768