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arXiv · 0909.0067

Bilinear biorthogonal expansions and the Dunkl kernel on the real line

L. D. Abreu·Ó. Ciaurri·J. L. Varona
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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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L. D. Abreu, Ó. Ciaurri, J. L. Varona. 2009-09-01. Bilinear biorthogonal expansions and the Dunkl kernel on the real line. https://doi.org/10.1016/j.exmath.2011.08.001

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