A solution to the Al-Salam--Chihara moment problem
arXiv:1812.01282 · doi:10.1007/978-3-030-10850-2_11
Abstract
We study the -hypergeometric difference operator on a particular Hilbert space. In this setting can be considered as an extension of the Jacobi operator for -Al-Salam--Chihara polynomials. Spectral analysis leads to unitarity and an explicit inverse of a -analog of the Jacobi function transform. As a consequence a solution of the Al-Salam--Chihara indeterminate moment problem is obtained.
22 pages