Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/7769
Title: The Reproducing Kernel Structure Arising from a Combination of Continuous and Discrete Orthogonal Polynomials into Fourier Systems
Authors: Abreu, Luís Daniel 
Issue Date: 2008
Citation: Constructive Approximation. 28:2 (2008) 219-235
Abstract: Abstract We study mapping properties of operators with kernels defined via a combination of continuous and discrete orthogonal polynomials, which provide 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, by establishing a link with Saitoh’s theory of linear transformations in Hilbert space. The results are illustrated with Fourier kernels with ultraspherical, 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/10316/7769
DOI: 10.1007/s00365-006-0657-0
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

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