Reflections on harmonic analysis of the Sierpiński gasket

Manfred Denker, Hiroshi Sato

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

Based on the geometric structure of the Sierpiński gasket, KIGAMI, established the harmonic analysis for the gasket analytically. On the other hand DENKER and SATO proved that the Sierpiński gasket S in IRN has a natural description as the Martin boundary for some canonical Markov chain on the word space. The aim of this paper is to reveal the connection between the harmonic analysis of the Markov chain and that of the Sierpiński gasket viewed as a Martin boundary, and to describe this analysis in terms of the Markov operator, the Martin kernel and the structure of the word space.

Original languageEnglish (US)
Pages (from-to)32-55
Number of pages24
JournalMathematische Nachrichten
Volume241
DOIs
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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