Biharmonic extensions on trees without positive potentials (Q633679)

A basic question in potential theory is the following: Given a function harmonic outside a compact set, is there a natural way to associate a global harmonic function to it? In the classical theory, this question is answered when the ambient space is an open subset of \(\mathbb{R}^n\), \(n\geq 2\). In the present paper, the analogous question for biharmonic functions on trees without positive potentials is studied.