Reflections on harmonic analysis of the Sierpinski gasket

被引：0

作者：

Denker, M

Sato, H

机构：

[1] Univ Gottingen, Inst Math Stochastik, D-37083 Gottingen, Germany

[2] Kyushu Univ, Grad Sch Math, Fukuoka 8128581, Japan

来源：

MATHEMATISCHE NACHRICHTEN | 2002年 / 241卷

关键词：

Sierpinski gasket; harmonic function; Laplace operator; Martin boundary;

D O I：

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

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Based on the geometric structure of the Sierpinski gasket, KIGAMI [10], [11] established the harmonic analysis for the gasket analytically. On the other hand DENKER and SATO [3] proved that the Sierpinski gasket S in R-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 Sierpinski 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.

引用

页码：32 / 55

页数：24