Riemann boundary value problem on quasidisks, Faber isomorphism and Grunsky operator
type: Item
instance of: scholarly article
title: Riemann boundary value problem on quasidisks, Faber isomorphism and Grunsky operator
zbMATH Open document ID: 1391.30054
author: Wolfgang Staubach
author: Eric Schippers
published in: Complex Analysis and Operator Theory
publication date: 2018-02-13T00:00:00Z
review text: Let \(\Gamma\) be a bounded Jordan curve in the complex plane. The authors prove that the Plemelj-Sokhotski jump decomposition is an isomorphism if and only if \(\Gamma\) is a quasicircle. They also show that the Bergman space of \(L^2\) harmonic one-forms is isomorphic to the direct sum of the holomorphic Bergman spaces if and only if \(\Gamma\) is quasicircle, and obtain new interpretations of the Grunsky and Schiffer operators.
reviewed by: Boris A. Kats
Mathematics Subject Classification ID: 30E25
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 6837876
zbMATH Keywords: Jordan curves
zbMATH Keywords: quasicircles
zbMATH Keywords: Plemelj-Sokhotski jump decomposition
zbMATH Keywords: Bergman space
zbMATH Keywords: Grunsky operator
zbMATH Keywords: Schiffer operator
MaRDI profile type: Publication
full work available at URL: s11785-016-0598-4
OpenAlex ID: W2536338359
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DOI: 10.1007/S11785-016-0598-4
description: scientific article; zbMATH DE number 6837876