q-Frames and Bessel Functions

A construction of frames is found depending on a parameter q by using Bessel functions. This is done via Cuntz algebras representations on L-q(2) ([0, 1], d mu(q)). We combine the use of q-hypergeometric functions with representation theory for the Cuntz relations in constructing explicit and iterative bases and frames in the Hilbert space L-q(2) (0, 1).