  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.
