Positive harmonic functions on biregular trees
Keywords:
Biregular tree, Maximal growth, Positive harmonic function
Abstract
We show that if f is a positive harmonic function on a biregular tree which has maximal growth along an infinite path in the tree, then every harmonic function g on the tree with 0 ≤ g ≤ f is a multiple of f, thus generalizing a result of Cartier about regular trees.
