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https://hdl.handle.net/10316/13647
Título: | Bilinear biorthogonal expansions and the spectrum of an integral operator | Autor: | Abreu, Luís Daniel Ciaurri, Óscar Varona, Juan Luis |
Palavras-chave: | Bilinear expansion; Biorthogonal expansion; Plane wave expansion; Sampling theorem; Fourier-Neumann expansion; Dunkl transform; Special functions; Q-special functions | Data: | 2009 | Editora: | Centro de Matemática da Universidade de Coimbra | Citação: | Pré-Publicações DMUC. 09-32 (2009) | Título da revista, periódico, livro ou evento: | Pré-Publicações DMUC | Número: | 09-32 | Local de edição ou do evento: | Coimbra | 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. Concerning applications, several new results are obtained. From the Dunkl analogue of Gegenbauer’s expansion of the plane wave, we derive sampling and Fourier-Neumann type expansions and an explicit closed formula for the spectrum of a right inverse of the Dunkl operator. This is done by stating the problem in such a way it is possible to use the technique due to Ismail and Zhang. Moreover, we provide a q-analogue of the Fourier-Neumann expansions in q-Bessel functions of the third type. In particular, we obtain a q-linear analogue of Gegenbauer’s expansion of the plane wave by using q-Gegenbauer polynomials defined in terms of little q-Jacobi polynomials. | URI: | https://hdl.handle.net/10316/13647 | Direitos: | openAccess |
Aparece nas coleções: | FCTUC Matemática - Vários |
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Ficheiro | Descrição | Tamanho | Formato | |
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Bilinear biorthogonal expansions and the spectrum of an integral operator.pdf | 281.74 kB | Adobe PDF | Ver/Abrir |
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