Reflections on harmonic analysis of the Sierpiński gasket

Manfred Denker; Hiroshi Sato

doi:10.1002/1522-2616(200207)241:1<32::AID-MANA32>3.0.CO;2-5

Reflections on harmonic analysis of the Sierpiński gasket

Manfred Denker
, Hiroshi Sato

Mathematics

Research output: Contribution to journal › Article › peer-review

15 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 IR^N 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 language	English (US)
Pages (from-to)	32-55
Number of pages	24
Journal	Mathematische Nachrichten
Volume	241
DOIs	https://doi.org/10.1002/1522-2616(200207)241:1<32::AID-MANA32>3.0.CO;2-5
State	Published - 2002

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1002/1522-2616(200207)241:1<32::AID-MANA32>3.0.CO;2-5

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abstract = "Based on the geometric structure of the Sierpi{\'n}ski gasket, KIGAMI, established the harmonic analysis for the gasket analytically. On the other hand DENKER and SATO proved that the Sierpi{\'n}ski 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 Sierpi{\'n}ski 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.",

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AU - Sato, Hiroshi

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AB - 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.

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JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

ER -

Reflections on harmonic analysis of the Sierpiński gasket

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