On the Study of the Klein-Gordon Equation in the Dunkl Setting

2023/05/22 by Gaidi, Mohamed, Bedhiafi, Mounir
#35B45 (Primary) 35C15 #42B15 #42B37 #47B90 (Secondary) #81Q05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.13039

Abstract

In Dunkl theory on ℝⁿ which generalizes classical Fourier analysis, we study the solution of the Klein-Gordon-equation defined by: ∂_t²u-Δ_ku=-m²u , u (x,0)=g(x) , ∂_tu(x,0)=f(x) with m > 0 and ∂_t²u is the second derivative of the solution u with respect to t and Δ_ku is the Dunkl Laplacian with respect to x where f and g the two functions in S(ℝⁿ) which surround the initial conditions. We obtain an integral representation for its solution which we gives some properties. As a specific result, we studied the associated energies to the Dunkl-Klein-Gordon equation.

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