Bilinear biorthogonal expansions and the Dunkl kernel on the real line |
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Authors: | Luí s Daniel Abreu,Ó scar Ciaurri,Juan Luis Varona |
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Affiliation: | 1. CMUC and Departamento de Matemática, Universidade de Coimbra, Faculdade de Ciências e Tecnologia (FCTUC), 3001-454 Coimbra, Portugal;2. CIME and Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain |
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Abstract: | 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. |
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Keywords: | primary, 94A20 secondary, 42A38, 42C10, 33D45 |
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