Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets

Mathematics Subject Classification: 42A38, 42C40, 33D15, 33D60This paper aims to study the q-wavelets and the continuous q-wavelet transforms, associated with the q-Bessel operator for a fixed q ∈]0, 1[. Using the q-Riemann-Liouville and the q-Weyl transforms, we give some relations between the continuous q-wavelet transform, studied in [3], and the continuous q-wavelet transform associated with the q-Bessel operator, and we deduce formulas which give the inverse operators of the q-Riemann-Liouville and the q-Weyl transforms

On Some Inequalities of Uncertainty Principles Type in Quantum Calculus

The aim of this paper is to generalize the q-Heisenberg uncertainty principles studied by , to state local uncertainty principles for the q-Fourier-cosine, the q-Fourier-sine, and the q-Bessel-Fourier transforms, then to provide an inequality of Heisenberg-Weyl-type for the qBessel-Fourier transform

On Some Inequalities of Uncertainty Principles Type in Quantum Calculus

The aim of this paper is to generalize the -Heisenberg uncertainty principles studied by Bettaibi et al. (2007), to state local uncertainty principles for the -Fourier-cosine, the -Fourier-sine, and the -Bessel-Fourier transforms, then to provide an inequality of Heisenberg-Weyl-type for the -Bessel-Fourier transform

On Some Inequalities of Uncertainty Principles Type in Quantum Calculus

The aim of this paper is to generalize the q-Heisenberg uncertainty principles studied by , to state local uncertainty principles for the q-Fourier-cosine, the q-Fourier-sine, and the q-Bessel-Fourier transforms, then to provide an inequality of Heisenberg-Weyl-type for the qBessel-Fourier transform