Autor(es):
Abreu, Luís Daniel 
Data: 2008
Identificador Persistente: http://hdl.handle.net/10316/7769
Origem: Estudo Geral - Universidade de Coimbra
Detalhes do Documento
The Reproducing Kernel Structure Arising from a Combination of Continuous and D...
Descrição
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
Tipo de Documento
Artigo
Idioma Inglês
Idioma Inglês
| Financiadores do RCAAP | |||||||
|
|
|
|
|
|
||