Boundary Theory on the Hata Tree

Ka Sing Lau, Sze Man Ngai

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 languageAmerican English
JournalNonlinear Analysis: Theory, Methods & Applications
Volume95
DOIs
StatePublished - Jan 1 2014

Disciplines

  • Education
  • Mathematics

Keywords

  • Fractal
  • Green function
  • Harmonic function
  • Hata tree
  • Markov chain
  • Martin boundary
  • Minimal Martin boundary

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