Bilinear biorthogonal expansions and the Dunkl kernel on the real line
- Abreu, L.D. 2
- Ciaurri, T. 1
- Varona, J.L. 1
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1
Universidad de La Rioja
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2
Universidade de Coimbra
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ISSN: 0723-0869
Ano de publicación: 2012
Volume: 30
Número: 1
Páxinas: 32-48
Tipo: Artigo
Outras publicacións en: Expositiones Mathematicae
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Resumo
We study an extension of the classical Paley-Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structure includes both sampling expansions and Fourier-Neumann type series as special cases, and it also provides a bilinear expansion for the Dunkl kernel (in the rank 1 case) which is a Dunkl analogue of Gegenbauer's expansion of the plane wave and the corresponding sampling expansions. In fact, we show how to derive sampling and Fourier-Neumann type expansions from the results related to the bilinear expansion for the Dunkl kernel. © 2011 Elsevier Ltd. All rights reserved.