Author(s):
Abreu, Luís Daniel 
Date: 2008
Persistent ID: http://hdl.handle.net/10316/7769
Origin: Estudo Geral - Universidade de Coimbra
Document details
The Reproducing Kernel Structure Arising from a Combination of Continuous and D...
Description
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. http://dx.doi.org/10.1007/s00365-006-0657-0
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. http://dx.doi.org/10.1007/s00365-006-0657-0
Document Type
Article
Language English
Language English
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