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https://hdl.handle.net/10316/13647
Title: | Bilinear biorthogonal expansions and the spectrum of an integral operator | Authors: | Abreu, Luís Daniel Ciaurri, Óscar Varona, Juan Luis |
Keywords: | Bilinear expansion; Biorthogonal expansion; Plane wave expansion; Sampling theorem; Fourier-Neumann expansion; Dunkl transform; Special functions; Q-special functions | Issue Date: | 2009 | Publisher: | Centro de Matemática da Universidade de Coimbra | Citation: | Pré-Publicações DMUC. 09-32 (2009) | Serial title, monograph or event: | Pré-Publicações DMUC | Issue: | 09-32 | Place of publication or event: | Coimbra | 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. 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 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
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Bilinear biorthogonal expansions and the spectrum of an integral operator.pdf | 281.74 kB | Adobe PDF | View/Open |
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