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dc.contributor.authorAbreu, Luís Daniel-
dc.contributor.authorCiaurri, Óscar-
dc.contributor.authorVarona, Juan Luis-
dc.identifier.citationPré-Publicações DMUC. 09-32 (2009)en_US
dc.description.abstractWe 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.en_US
dc.publisherCentro de Matemática da Universidade de Coimbraen_US
dc.subjectBilinear expansionen_US
dc.subjectBiorthogonal expansionen_US
dc.subjectPlane wave expansionen_US
dc.subjectSampling theoremen_US
dc.subjectFourier-Neumann expansionen_US
dc.subjectDunkl transformen_US
dc.subjectSpecial functionsen_US
dc.subjectQ-special functionsen_US
dc.titleBilinear biorthogonal expansions and the spectrum of an integral operatoren_US
degois.publication.titlePré-Publicações DMUCen_US
item.fulltextCom Texto completo-
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