Elements of harmonic analysis related to the third basic zero order Bessel function

This paper is devoted to the study of some q-harmonic analysis related to the third q-Bessel function of order zero.We establish a product formula leading to a q-translation with some positive kernel. As an application, we provide a q-analogue of the continuous wavelet transform related to this harmonic analysis. © 2008 Elsevier Inc. All rights reserved.