On the convolution product of the distributional kernel Kα,β,γ,ν

Abstract

We introduce a distributional kernel Kα,β,γ,ν which is related to the operator ⊕ k iterated k times and defined by , where p + q = n is the dimension of the space ℝ n of the n‐dimensional Euclidean space, x = (x1, x2, …, xn) ∈ ℝ n, k is a nonnegative integer, and α, β, γ, and ν are complex parameters. It is found that the existence of the convolution is depending on the conditions of p and q.