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Riemann boundary value problem on quasidisks, Faber isomorphism and Grunsky operator.
Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2018 (English)In: Complex Analysis and Operator Theory, ISSN 1661-8254, E-ISSN 1661-8262, Vol. 12, no 2, p. 325-354Article in journal (Refereed) Published
Abstract [en]

Let Γ be a bounded Jordan curve with complementary components Ω ± . Weshow that the jump decomposition is an isomorphism if and only if Γ is a quasicircle. Wealso show that the Bergman space of L 2 harmonic one-forms on Ω + is isomorphic to thedirect sum of the holomorphic Bergman spaces on Ω + and Ω − if and only if Γ is a quasicircle.This allows us to derive various relations between a reflection of harmonic functions inquasicircles and the jump decomposition on the one hand, and the Grunsky operator, Faberseries and kernel functions of Schiffer on the other hand. It also leads to new interpretationsof the Grunsky and Schiffer operators. We show throughout that the most general settingfor these relations is quasidisks.

Place, publisher, year, edition, pages
2018. Vol. 12, no 2, p. 325-354
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:uu:diva-304007DOI: 10.1007/s11785-016-0598-4ISI: 000423719900001OAI: oai:DiVA.org:uu-304007DiVA, id: diva2:975119
Funder
Wenner-Gren Foundations
Available from: 2016-09-28 Created: 2016-09-28 Last updated: 2018-03-15Bibliographically approved

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Staubach, Wolfgang

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