On the operator ⊕k related to the wave equation and Laplacian

摘要

In this paper, we study the Green function of the operator ⊕k, iterated k-times and is defined bywhere p+q=n is the dimension of the space Cn, where C is a complex field, x=(x1,x2,…,xn)∈Cn and k is a nonnegative integer. At first we study the elementary solution or the Green function of the operator ⊕k and then such a solution is related to the solution of the wave equation and the Laplacian. We found that the relationships of such solutions depending on the conditions of p, q and k.