Some aspects of the classical potential theory on trees.

Abstract

Potential theory on a Cartier tree T is developed on the lines of the classical and the axiomatic theories on harmonic spaces. The harmonic classifications of such trees are considered; the notion of a subordinate structure on T is introduced to consider more generally the potential theory on T associated with the Schrodinger equation on T; polysuperharmonic functions and polypotentials on T are defined and a Riesz-Martin representation for positive polysuperharmonic function is obtained