Title

Boundary Theory on the Hata Tree

Document Type

Article

Publication Date

2014

Publication Title

Nonlinear Analysis: Theory, Methods & Applications

DOI

10.1016/j.na.2013.08.013

Abstract

We prove that for a certain Markov chain on the symbolic space of the Hata tree K, the Martin boundary M is homeomorphic to the trunk of the Hata tree, and the minimal Martin boundary is the post-critical set {12, 1, 2}, which corresponds to the three vertices of the trunk. Moreover, the class of P-harmonic functions on M coincides with Kigami’s class of harmonic functions on K.

Share

COinS