Calderon's reproducing formula and uncertainty principle for the continuous wavelet transform associated with the q-Bessel operator

摘要

In this paper, we present some new elements of harmonic analysis related to the q-Bessel Fourier transform introduced earlier in Dhaouadi (Bull Math Anal Appl 5(2):42-60, 2013), Dhaouadi et al. (J Inequal Pure Appl Math 7(5):171, 2006), we define and study the q-wavelet and the continuous q-wavelet transform associated with this harmonic analysis. Thus, some results (Plancherel's formula, inversion formula, etc.) are established. Next, we prove a Caldern's formula and an analogue of Heisenberg's inequality for the continuous q-wavelet transform.