On the solution of the n-dimensional diamond klein-gordon operator and its convolution

Abstract

In this article, we introduce the diamond Klein-Gordon operator iterated k times, which is defined by where p + q = n is the dimension of ℝ n, for all x = (x 1, x 2,..., x n) ∈ ℝ n, m ≥0 and non-negative integers k. Our aim is to study the fundamental solution of the operator (◇ + m 2) k, to which we will refer as the diamond Klein-Gordon kernel. Moreover, we will study the convolution of this kernel. © 2012 Pushpa Publishing House.