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.
Original language | American English |
---|---|
Journal | Nonlinear Analysis: Theory, Methods & Applications |
Volume | 95 |
DOIs | |
State | Published - Jan 1 2014 |
Disciplines
- Education
- Mathematics
Keywords
- Fractal
- Green function
- Harmonic function
- Hata tree
- Markov chain
- Martin boundary
- Minimal Martin boundary