%0 Journal Article
%T Bilinear biorthogonal expansions and the Dunkl kernel on the real line
%A L. D. Abreu
%A ио. Ciaurri
%A J. L. Varona
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0909.0067v3