Local admissible convergence of harmonic functions on non-homogeneous trees
Volume 118 / 2010
Colloquium Mathematicum 118 (2010), 419-444 MSC: Primary 05C05; Secondary 31A20, 60J45. DOI: 10.4064/cm118-2-5
We prove admissible convergence to the boundary of functions that are harmonic on a subset of a non-homogeneous tree equipped with a transition operator that satisfies uniform bounds suitable for transience. The approach is based on a discrete Green formula, suitable estimates for the Green and Poisson kernel and an analogue of the Lusin area function.