dunkl operator
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2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shrideh Al-Omari ◽  
Hassan Almusawa ◽  
Kottakkaran Sooppy Nisar

AbstractIn this paper we investigate certain integral operator involving Jacobi–Dunkl functions in a class of generalized functions. We utilize convolution products, approximating identities, and several axioms to allocate the desired spaces of generalized functions. The existing theory of the Jacobi–Dunkl integral operator (Ben Salem and Ahmed Salem in Ramanujan J. 12(3):359–378, 2006) is extended and applied to a new addressed set of Boehmians. Various embeddings and characteristics of the extended Jacobi–Dunkl operator are discussed. An inversion formula and certain convergence with respect to δ and Δ convergences are also introduced.



2021 ◽  
Vol 45 (01) ◽  
pp. 39-46
Author(s):  
EL MEHDI LOUALID ◽  
AZZEDINE ACHAK ◽  
RADOUAN DAHER

The Q-Fourier-Dunkl transform satisfies some uncertainty principles in a similar way to the Euclidean Fourier transform. By using the heat kernel associated to the Q-Fourier-Dunkl operator, we establish an analogue of Beurling’s theorem for the Q-Fourier-Dunkl transform ℱQ on ℝ.



2020 ◽  
Vol 51 (4) ◽  
pp. 1533-1554
Author(s):  
Mehdi Lachiheb ◽  
Abdesselem Gasmi
Keyword(s):  






Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 794
Author(s):  
Rabha W. Ibrahim ◽  
Rafida M. Elobaid ◽  
Suzan J. Obaiys

Quantum inequalities (QI) are local restraints on the magnitude and range of formulas. Quantum inequalities have been established to have a different range of applications. In this paper, we aim to introduce a study of QI in a complex domain. The idea basically, comes from employing the notion of subordination. We shall formulate a new q-differential operator (generalized of Dunkl operator of the first type) and employ it to define the classes of QI. Moreover, we employ the q-Dunkl operator to extend the class of Briot–Bouquet differential equations. We investigate the upper solution and exam the oscillation solution under some analytic functions.



2020 ◽  
Vol 35 (1) ◽  
pp. 043
Author(s):  
Azzedine Achak ◽  
Radouan Daher ◽  
Najat Safouane ◽  
El Mehdi Loualid

The Q-Fourier-Dunkl transform satisfies some uncertainty principles in a similar way to the Euclidean Fourier transform. By using theheat kernel associated to the Q-Fourier-Dunkl operator, we have established an analogue of Cowling-Price, Miyachi and Morgan theorems on $\mathbb{R}$ by using the heat kernel associated to the Q-Fourier-Dunkl transform.





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