GREEN’S FORMULA AND FLUX AT INFINITY ON A TREE WITHOUT POSITIVE POTENTIAL

Ibtesam Bajunaid (Saudi Arabia)

Received January 21, 2008

Abstract

The discrete version of the generalized form of Green’s formula is the basic tool to introduce the notion of flux which leads to many results on potential theory. In this article, we consider Green’s formula and flux on Cartier trees whose nearest-neighbor transition probabilities are defined by recurrent random walks.

Keywords and phrases: flux at infinity, Dirichlet problem.