A Poisson formula for harmonic functions on the Sierpiński gasket

Manfred Heinz Denker, Susanne Koch

Research output: Contribution to journalArticle

Abstract

We show a Poisson formula for bounded harmonic functions φ on the Sierpmski gasket y. We construct a boundary (∑, v), a measurable action of a semigroup W on ∑ and a map r: W y, such that for every bounded harmonic function φ on y φr(w))∫ Ψ(wς)v(dς) where Ψ: φ → IR is some bounded measurable function.

Original languageEnglish (US)
Pages (from-to)435-448
Number of pages14
JournalForum (Germany)
Volume12
Issue number4
StatePublished - May 1 2000

All Science Journal Classification (ASJC) codes

  • Sociology and Political Science
  • Social Sciences(all)

Cite this

Denker, M. H., & Koch, S. (2000). A Poisson formula for harmonic functions on the Sierpiński gasket. Forum (Germany), 12(4), 435-448.