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On the radial projection of harmonic measure. (Russian) Zbl 0791.31003
Marchenko, V. A. (ed.), Operator theory, subharmonic functions. Collection of scientific works. Kiev: Naukova Dumka. 95-102 (1991).
Let \(D\) denote a domain in \(\mathbb{C}\) containing the origin, \(E\) a part of the boundary of \(D\), \(\widehat{E}\) the radial projection of \(E\) on the unit circle, \(\widehat{\omega}_ D(\widehat{E}) = \omega(0,E,D)\), the harmonic measure of \(E\) with respect to \(D\). Let \(m\) denote a probability measure on the unit circle.
The question studied here is whether there exists a domain \(D\) such that \(m(\widehat{E}) = \omega(0,E,D)\). This is solved with NASC in the class of star-like domains \(D\). Applications are given to the growth of subharmonic functions [cf. the author, Sov. Math., Dokl. 41, No. 3, 460- 462 (1990); translation from Dokl. Akad. Nauk SSSR 312, No. 3, 536-538 (1990; Zbl 0722.31001)].
For the entire collection see [Zbl 0752.00029].

MSC:
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
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