On Iversen's property and the existence of bounded analytic functions
type: Item
instance of: scholarly article
title: On Iversen's property and the existence of bounded analytic functions
zbMATH Open document ID: 0547.30036
author: Zenjiro Kuramochi
published in: Hokkaido Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: Let R be a Riemann surface and f be a meromorphic function on R. If for any domain V of \({\bar {\mathbb{C}}}\) every component of \(f^{-1}(V)\) covers V up to a set of capacity zero then f is said to have the C.I. property. The author denotes by \(P_ I\) the class of Riemann surfaces R such that every meromorphic function on R possesses the C.I. property and by \(P_{HI}\) the class of Riemann surfaces R such that every holomorphic function on R possesses the C.I. property. Riemann surfaces belonging to \(P_{HI}\backslash P_ I\) and \(P_ I\backslash O_ G\) are constructed. The Martin and the Kuramochi ideal boundaries play an important part in these constructions.
Mathematics Subject Classification ID: 30F20
Mathematics Subject Classification ID: 30F25
zbMATH DE Number: 3871746
zbMATH Keywords: Martin ideal boundary
zbMATH Keywords: Kuramochi ideal boundaries
reviewed by: Corneliu Constantinescu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381757774
OpenAlex ID: W1990410643
DOI: 10.14492/HOKMJ/1381757774
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description: scientific article; zbMATH DE number 3871746