Wavelet Transforms Associated With the Basic Bessel Operator

Fitouhi, Ahmed; Bettaibi, Neji; Binous, Wafa

Wavelet Transforms Associated With the Basic Bessel Operator

Authors

Fitouhi, Ahmed

Bettaibi, Neji

Binous, Wafa

Description

This paper aims to study the $q$-wavelet and the $q$-wavelet transforms, associated with the $q$-Bessel operator for a fixed $q\in ]0, 1[$. As an application, an inversion formulas of the $q$-Riemann-Liouville and $q$-Weyl transforms using $q$-wavelets are given. For this purpose, we shall attempt to extend the classical theory by giving their $q$-analogues.
24 pages