J. Aust. Math. Soc.  75 (2003), 145-151
On the distribution of harmonic measure on simply connected planar domains

Dimitrios Betsakos
  Department of Mathematics
  Aristotle University of Thessaloniki
  54124 Thessaloniki
  Greece
  betsakos@auth.gr
and
Alexander Yu. Solynin
  Steklov Mathematical Institute
  St. Petersburg Branch
  Russian Academy of Sciences
  Fontanka 27
  191011 St. Petersburg
  Russia
  solynin@pdmi.ras.ru


Abstract
For a simply connected planar domain $D$ with $0\in D$ and $\operatorname{dist} (0,\partial D)=1$, let $h_D(r)$ be the harmonic measure of $\partial D\cap \{|z|\leq r\}$ evaluated at $0$. The function $h_D(r)$ 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.
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