Boundary theory on the Hata tree
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AbstractWe 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 {1(2) over dot, (1) over dot, (2) over dot}, 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. (C) 2013 Elsevier Ltd. All rights reserved.
All Author(s) ListLau KS, Ngai SM
Journal nameNonlinear Analysis: Theory, Methods and Applications
Detailed descriptionTo ORKTS:
Year2014
Month1
Day1
Volume Number95
PublisherElsevier
Pages292 - 307
ISSN0362-546X
eISSN1873-5215
LanguagesEnglish-United Kingdom
KeywordsFractal; Green function; Harmonic function; Hata tree; Markov chain; Martin boundary; Minimal Martin boundary
Web of Science Subject CategoriesMathematics; MATHEMATICS; Mathematics, Applied; MATHEMATICS, APPLIED

Last updated on 2021-14-01 at 23:31