A Poisson formula for harmonic functions on the Sierpiński gasket

Manfred Denker; Susanne Koch

A Poisson formula for harmonic functions on the Sierpiński gasket

Manfred Denker
, Susanne Koch

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	435-448
Number of pages	14
Journal	Forum (Germany)
Volume	12
Issue number	4
State	Published - May 1 2000

All Science Journal Classification (ASJC) codes

Sociology and Political Science
General Social Sciences

Cite this

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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.",

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N2 - 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.

AB - 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.

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M3 - Article

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A Poisson formula for harmonic functions on the Sierpiński gasket

Abstract

All Science Journal Classification (ASJC) codes

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