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On the study of the Klein–Gordon equation in the Dunkl setting
https://doi.org/10.26907/0021-3446-2025-7-3-19
Abstract
In Dunkl theory on \BbbR n which generalizes classical Fourier analysis, we study the solution of the Klein–Gordon-equation defined by: Მ2t u - Δku = - m2u, u(x, 0) = g(x), Მtu(x, 0) = f(x), где m > 0, а Მ2t u denoting the second derivative of the solution u with respect to t, and Δku u the Dunkl Laplacian with respect to x where f and g being two functions in Ѕ(Rn), defining the initial conditions. An integral representation for its solution is obtained, which makes it possible to study certain properties. As a specific result, the energies associated with the Dunkl–Klein–Gordon equation are studied.
About the Authors
M. Gaidi
Universit´e Tunis El Manar, El Manar I, 2092
Tunisia
Tunisia
Mohamed Gaidi
El Manar I, 2092
M. Bedhiafi
Universit´e Tunis El Manar;
Universit´e Tunis
Tunisia
Tunisia
Mounir Bedhiafi
El Manar I, 2092,
Rue Jawaher Lel Nehru, Montfleury, 1089
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Review
For citations:
Gaidi M., Bedhiafi M. On the study of the Klein–Gordon equation in the Dunkl setting. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;(7):3-19. (In Russ.) https://doi.org/10.26907/0021-3446-2025-7-3-19
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