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- Publisher
- de Gruyter
- Copyright
- Copyright © 2000 by Walter de Gruyter GmbH & Co. KG
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/form.2000.013
- Publisher site
- See Article on Publisher Site
Abstract
Forum Math. 12 (2000), 435±448 ( de Gruyter 2000 Manfred Denker and Susanne Koch* (Communicated by Michael Brin)  Abstract. We show a Poisson formula for bounded harmonic functions p on the Sierpinski ~ ~ ~ gasket S. We construct a boundary Y n, a measurable action of a semigroup W on and a map q X W 3 S, such that for every bounded harmonic function p on S pqw gwx~dxY n ~ where g X 3 R is some bounded measurable function. 1991 Mathematics Subject Classi®cation: 28A80, 60J10. 1 Introduction  Kigami ([K1]) de®ned harmonicity for continuous functions on the Sierpinski gasket together with a Laplace operator h such that hp 0 if and only if p is harmonic (see also [K2]). His de®nition is of purely geometric nature. There are several other descriptions of this class of functions ([M], [W] among others). Recently, it has been shown in [DS1] and [DS3] that harmonic functions have an integral representation using the Martin kernel of a certain canonical random walk. In this note we provide a new description proving an integral representation, which may be considered as a dynamic Poisson formula in analogy with [Fu]. Let W
Journal
Forum Mathematicum – de Gruyter
Published: May 29, 2000