A Poisson formula for harmonic functions on the Sierpiński gasket

Manfred Denker; Susanne Koch

doi:10.1515/form.2000.013

A Poisson formula for harmonic functions on the Sierpiński gasket

Manfred Denker
, Susanne Koch

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	435-448
Number of pages	14
Journal	Forum Mathematicum
Volume	12
Issue number	4
DOIs	https://doi.org/10.1515/form.2000.013
State	Published - 2000

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1515/form.2000.013

Cite this

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title = "A Poisson formula for harmonic functions on the Sierpi{\'n}ski gasket",

abstract = "We show a Poisson formula for bounded harmonic functions Φ on the Sierpi{\'n}ski gasket S. We construct a boundary ({\~Σ}, {\~ν}), a measurable action of a semigroup W on {\~Σ} and a map Γ: W → S, such that for every bounded harmonic function Φ on S Φ(Γ(w)) = ∫{\~Σ} Ψ(wξ){\~ν}(dξ), where Ψ : {\~Σ} → ℝ is some bounded measurable function.",

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AU - Koch, Susanne

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AB - 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.

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JF - Forum Mathematicum

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ER -

A Poisson formula for harmonic functions on the Sierpiński gasket

Abstract

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