On the distribution related to the ultra-hyperbolic equations

In this paper we consider the distribution eαt□kδ where α is a constant and α = (α1,α2,…,αn) ∈ Rn the n-dimensional Euclidean space and the variable t = (t1,t2,…,tn) ∈ Rn and □k is the n-dimensional ultra-hyperbolic operator iterated k-times, δ is the Dirac-delta distribution with □0δ = δ and □1δ = □δ. st, all properties of eαt□kδ are studied and after that we study the application of eαt□kδ for solving the elementary solution of the equation of the ultra-hyperbolic type by using the convolution method.