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) |
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Pages (from-to) | 435-448 |
Number of pages | 14 |
Journal | Forum Mathematicum |
Volume | 12 |
Issue number | 4 |
DOIs | |
State | Published - 2000 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics