Centre for Mathematics, University of Coimbra

<Reference List>
Type:	Preprint
National /International:	International
Title:	The reproducing kernel structure associated to Fourier type systems and their quantum analogues
Publication Date:	2005
Authors:	- Luís Daniel Abreu
Abstract:	We study mapping properties of operators with kernels defined via an abstract formulation of quantum (q-)Fourier type systems. We prove Ismail's conjecture regarding the existence of a reproducing kernel structure behind these kernels. The results are illustrated with Fourier kernels with ultraspherical and Jacobi weights, their continuous q-extensions and generalizations. As a byproduct of this approach, a new class of sampling theorems is obtained, as well as Neumann type expansions in Bessel and q-Bessel functions.
Institution:	DMUC 05-27
Online version:	http://www.mat.uc.pt...prints/eng_2005.html
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