GREEN’S IDENTITY, FUNDAMENTAL SOLUTION AND DIRICHLET PROBLEM OF THE DIAMOND OPERATOR

B. Chalermpon (Thailand) and A. Kananthai (Thailand)

Received March 21, 2007

Abstract

In this paper, we study Green’s identity, fundamental solution and Dirichlet problem of the Diamond operator, denoted by  and defined by  is the dimension of Euclidian space  We obtain such fundamental solution as a tempered distribution in the form of convolution.

Keywords and phrases: Diamond operator, Green’s identity, fundamental solution.