Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Bilinear Biorthogonal expansions and the spectrum of an integral operator
Publication Date:	2009
Authors:	- Luís Daniel Abreu - Óscar Ciaurri - Juan Luis Varona
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.
Institution:	DMUC 09-32
Online version:	http://www.mat.uc.pt...prints/eng_2009.html
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