Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/11378
Title: The reproducing kernel structure associated to Fourier type systems and their quantum analogues
Authors: Abreu, Luís Daniel 
Keywords: Reproducing kernel; q-Fourier series; Orthogonal polynomials; Basic hypergeometric functions; Sampling theorems
Issue Date: 2005
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 05-27 (2005)
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.
URI: http://hdl.handle.net/10316/11378
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Nacionais

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