A Poisson formula for harmonic functions on the Sierpiński gasket

Manfred Denker, Susanne Koch

Research output: Contribution to journalArticle

2 Citations (Scopus)

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

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Harmonic functions
Harmonic Functions
Siméon Denis Poisson
Measurable function
Semigroup

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Denker, Manfred ; Koch, Susanne. / A Poisson formula for harmonic functions on the Sierpiński gasket. In: Forum Mathematicum. 2000 ; Vol. 12, No. 4. pp. 435-448.
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A Poisson formula for harmonic functions on the Sierpiński gasket. / Denker, Manfred; Koch, Susanne.

In: Forum Mathematicum, Vol. 12, No. 4, 01.01.2000, p. 435-448.

Research output: Contribution to journalArticle

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