A Poisson formula for harmonic functions on the Sierpinski gasket

Authors
Denker, M Koch, S
Citation
M. Denker et S. Koch, A Poisson formula for harmonic functions on the Sierpinski gasket, FORUM MATH, 12(4), 2000, pp. 435-448
Citations number
9
Categorie Soggetti
Mathematics
Journal title
FORUM MATHEMATICUM
ISSN journal
09337741 → ACNP
Volume
12
Issue
4
Year of publication
2000
Pages
435 - 448
Database
ISI
SICI code
0933-7741(2000)12:4<435:APFFHF>2.0.ZU;2-8
Abstract
We show a Poisson formula for bounded harmonic functions Phi on the Sierpin ski gasket Y. We construct a boundary (<(Sigma)over tilde>, <(nu)over tilde >, S), a measurable action of a semigroup W on <(Sigma)over tilde> and a ma p Gamma: W --> Y, such that for every bounded harmonic function Phi on Y Ph i(Gamma (w)) = integral(<(Sigma)over tilde>) Psi(w xi)<(nu)over tilde>(d xi ), where Psi : <(Sigma)over tilde> --> R is some bounded measurable functio n.