8 research outputs found
Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets
No full textMathematics 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
Paley–Wiener theorem for the q-Bessel transform and associated q-sampling formula
No full textAbstractThis paper establishes a Paley–Wiener theorem related to the q-Bessel transform and gives the associated q-sampling formula with qn,n∈Z as sampling points
Elements of harmonic analysis related to the third basic zero order Bessel function
No full textAbstractThis 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
On Some Inequalities of Uncertainty Principles Type in Quantum Calculus
No full textThe 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
No full textThe 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
No full textThe 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
