BESSEL FUNCTIONS AND CUNTZ ALGEBRAS REPRESENTATIONS

Orthogonality relations for Bessel functions are exploited to construct representations of the Cuntz algebra acting on L(2)((0, infinity)). This class of representations turns out to be unitarily equivalent to a class of permutative representations as those in [3]. We then generalize to obtain a class of q-dependent representations using the third Jackson q-Bessel functions.