Local admissible convergence of harmonic functions on non-homogeneous trees
Massimo A. Picardello (2010)
Colloquium Mathematicae
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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.