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.
Recommended Citation
Lau, Ka-Sing, Sze-Man Ngai.
2014.
"Boundary Theory on the Hata Tree."
Nonlinear Analysis: Theory, Methods & Applications, 95: 292-307.
doi: 10.1016/j.na.2013.08.013
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/131
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