Sampling theorems associated with biorthogonal q-Bessel functions

This paper deals with the derivation of sampling theorems associated with q-biorthogonal systems. We derive interpolation expansions for q-Hankel transforms whose kernels are the second-type q-Bessel functions J _ν⁽²⁾ (z; q), ν > 0, 0 < q < 1. We investigate the eigenvalue problem whose solutions are the q-Bessel functions as well as its adjoint. Special cases and applications involving the associated q-sine function are given. The results are based on the conjecture that a family of q-Bessel functions of the second kind is a Riesz basis. Clues are given to support our claim.