Chefai Soumaya | Faculté des Sciences de Tunis (original) (raw)
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Papers by Chefai Soumaya
Asian-European Journal of Mathematics
Based on the [Formula: see text]-Mellin operator properties, we verify rigorously new class of [F... more Based on the [Formula: see text]-Mellin operator properties, we verify rigorously new class of [Formula: see text]-index transforms. Moreover, we establish a convolution operator and inversion formulas. As applications, we give new transformations with the hypergeometric functions kernel.
Journal of Pseudo-Differential Operators and Applications, 2017
This paper deals firstly with some q-harmonic analysis properties for the q-windowed Bessel Fouri... more This paper deals firstly with some q-harmonic analysis properties for the q-windowed Bessel Fourier transform related to the q-Bessel function of the third kind as Plancherel formula, inversion formula in L q,2,ν. Secondly, we give a weak uncertainty principle for it and we show that the portion of the q-windowed Bessel Fourier transform lying outside some set of finite measure cannot be arbitrarily too small. Then, we verify a version of Heisenberg-Pauli-Weyl type uncertainty inequalities for the q-windowed Bessel Fourier transform and its generalization. Finally, using the kernel reproducing theory, given by Saitoh (Theory of reproducing kernels and its applications. Longman Scientific and Technical, Harlow, 1988), we will be able to realize the natural and powerful approximation problems that lead to the q-windowed Bessel Fourier transform inverses. Keywords q-Bessel function of the third kind • q-Bessel Fourier transform • Uncertainty principles • Heisenberg-Pauli-Weyl inequality • Time-frequency concentration • Hilbert spaces with reproducing kernel • Approximations • Practical real inversion formula 1 Introduction Time-frequency analysis plays a central role in signal analysis. It is often studied to the signal's Fourier transform, which reliably yields frequency information, but without any localization in time. The time-frequency resolution is usually associated with the windowed Fourier transform also known as the (continuous) Gabor transform, B Soumaya Chefai
In this paper we study in quantum calculus the theory of inverse problem and approximation in a l... more In this paper we study in quantum calculus the theory of inverse problem and approximation in a large class of Hilbert spaces with reproducing kernels. 2000 AMS Mathematics Subject Classification—Primary : 33D15,47A05.
Asian-European Journal of Mathematics
Based on the [Formula: see text]-Mellin operator properties, we verify rigorously new class of [F... more Based on the [Formula: see text]-Mellin operator properties, we verify rigorously new class of [Formula: see text]-index transforms. Moreover, we establish a convolution operator and inversion formulas. As applications, we give new transformations with the hypergeometric functions kernel.
Journal of Pseudo-Differential Operators and Applications, 2017
This paper deals firstly with some q-harmonic analysis properties for the q-windowed Bessel Fouri... more This paper deals firstly with some q-harmonic analysis properties for the q-windowed Bessel Fourier transform related to the q-Bessel function of the third kind as Plancherel formula, inversion formula in L q,2,ν. Secondly, we give a weak uncertainty principle for it and we show that the portion of the q-windowed Bessel Fourier transform lying outside some set of finite measure cannot be arbitrarily too small. Then, we verify a version of Heisenberg-Pauli-Weyl type uncertainty inequalities for the q-windowed Bessel Fourier transform and its generalization. Finally, using the kernel reproducing theory, given by Saitoh (Theory of reproducing kernels and its applications. Longman Scientific and Technical, Harlow, 1988), we will be able to realize the natural and powerful approximation problems that lead to the q-windowed Bessel Fourier transform inverses. Keywords q-Bessel function of the third kind • q-Bessel Fourier transform • Uncertainty principles • Heisenberg-Pauli-Weyl inequality • Time-frequency concentration • Hilbert spaces with reproducing kernel • Approximations • Practical real inversion formula 1 Introduction Time-frequency analysis plays a central role in signal analysis. It is often studied to the signal's Fourier transform, which reliably yields frequency information, but without any localization in time. The time-frequency resolution is usually associated with the windowed Fourier transform also known as the (continuous) Gabor transform, B Soumaya Chefai
In this paper we study in quantum calculus the theory of inverse problem and approximation in a l... more In this paper we study in quantum calculus the theory of inverse problem and approximation in a large class of Hilbert spaces with reproducing kernels. 2000 AMS Mathematics Subject Classification—Primary : 33D15,47A05.