Reflections on harmonic analysis of the Sierpinski gasket

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.