Abstract
We study the q-hypergeometric difference operator L on a particular Hilbert space. In this setting L can be considered as an extension of the Jacobi operator for q −1-Al-Salam–Chihara polynomials. Spectral analysis leads to unitarity and an explicit inverse of a q-analog of the Jacobi function transform. As a consequence a solution of the Al-Salam–Chihara indeterminate moment problem is obtained.
This paper is dedicated to Ben de Pagter on the occasion of his 65th birthday
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Groenevelt, W. (2019). A Solution to the Al-Salam–Chihara Moment Problem. In: Buskes, G., et al. Positivity and Noncommutative Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-10850-2_11
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DOI: https://doi.org/10.1007/978-3-030-10850-2_11
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