A Poisson formula for harmonic functions on the Sierpiński gasket

Manfred Denker, Susanne Koch

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We show a Poisson formula for bounded harmonic functions Φ on the Sierpiński gasket S. We construct a boundary (Σ̃, ν̃), a measurable action of a semigroup W on Σ̃ and a map Γ: W → S, such that for every bounded harmonic function Φ on S Φ(Γ(w)) = ∫Σ̃ Ψ(wξ)ν̃(dξ), where Ψ : Σ̃ → ℝ is some bounded measurable function.

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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