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On the distribution of harmonic measure on simply connected planar domains

Published online by Cambridge University Press:  09 April 2009

Dimitrios Betsakos
Affiliation:
Department of Mathematics Aristotle University of Thessaloniki54124 ThessalonikiGreece e-mail: [email protected]
Alexander Yu. Solynin
Affiliation:
Steklov Mathematical InstituteSt. Petersburg Branch Russian Academy of Sciences Fontanka 27 191011 St. PetersburgRussia e-mail: [email protected]
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Abstract

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For a simply connected planar domain D with 0 ∈ D and dist(0, ∂D) = 1, let hD(r) be the harmonic measure of ∂ D ∩{|Z| ≤ r} evaluated at 0. The function hD(r) is the distribution of harmonic measure. It has been studied by B. L. Walden and L. A. Ward. We continue their study and answer some questions raised by them by constructing domains with pre-specified distribution.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2003

References

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