Sierpiński Gasket as a Martin Boundary I: Martin Kernels

Manfred Denker, Hiroshi Sato

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We show that a Sierpiński gasket in N dimension is homeomorphic to the minimal Martin boundary of some canonical Markov chain. This provides a new class of examples for the boundary theory of Markov chains and the basis for a harmonic analysis on p.c.f. fractal structures.

Original languageEnglish (US)
Pages (from-to)211-232
Number of pages22
JournalPotential Analysis
Volume14
Issue number3
DOIs
StatePublished - 2001

All Science Journal Classification (ASJC) codes

  • Analysis

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