Dirichlet-to-Robin Operators via Composition Semigroups

Dirichlet-to-Robin Operators via Composition Semigroups Complex Anal. Oper. Theory Complex Analysis https://doi.org/10.1007/s11785-018-0806-5 and Operator Theory Dirichlet-to-Robin Operators via Composition Semigroups Lars Perlich Received: 6 September 2017 / Accepted: 26 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract We show well-posedness for an evolution problem associated with the Dirichlet-to-Robin operator for certain Robin boundary data. Moreover, it turns out that the semigroup generated by the Dirichlet-to-Robin operator is closely related to a weighted semigroup of composition operators on an appropriate Banach space of analytic functions. Keywords Composition operators · Spaces of holomorphic functions · Dirichlet-to-Neumann · Dirichlet-to-Robin Mathematics Subject Classification 47B38 · 47B33 · 47D06 1 Introduction In recent years, the Dirichlet-to-Neumann operator has been studied intensively. In the beginning of the 20th century, these operators were dealt with theoretically, while in the 1980s and 1990s they were used to analyze inverse problems to determine coefficients of a differential operator. These problems apply, e.g., to image techniques in medicine and also to find defects in materials. Communicated by Daniel Aron Alpay. The author is supported by Sächsisches Landesstipendium. B Lars Perlich lars.perlich@mailbox.tu-dresden.de Institut für Analysis, Technische Universität Dresden, Zellescher Weg 12-14, 01069 Dresden, Germany L. Perlich According to Arendt and http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Complex Analysis and Operator Theory Springer Journals

Dirichlet-to-Robin Operators via Composition Semigroups

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general; Operator Theory; Analysis
ISSN
1661-8254
eISSN
1661-8262
D.O.I.
10.1007/s11785-018-0806-5
Publisher site
See Article on Publisher Site

Abstract

Complex Anal. Oper. Theory Complex Analysis https://doi.org/10.1007/s11785-018-0806-5 and Operator Theory Dirichlet-to-Robin Operators via Composition Semigroups Lars Perlich Received: 6 September 2017 / Accepted: 26 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract We show well-posedness for an evolution problem associated with the Dirichlet-to-Robin operator for certain Robin boundary data. Moreover, it turns out that the semigroup generated by the Dirichlet-to-Robin operator is closely related to a weighted semigroup of composition operators on an appropriate Banach space of analytic functions. Keywords Composition operators · Spaces of holomorphic functions · Dirichlet-to-Neumann · Dirichlet-to-Robin Mathematics Subject Classification 47B38 · 47B33 · 47D06 1 Introduction In recent years, the Dirichlet-to-Neumann operator has been studied intensively. In the beginning of the 20th century, these operators were dealt with theoretically, while in the 1980s and 1990s they were used to analyze inverse problems to determine coefficients of a differential operator. These problems apply, e.g., to image techniques in medicine and also to find defects in materials. Communicated by Daniel Aron Alpay. The author is supported by Sächsisches Landesstipendium. B Lars Perlich lars.perlich@mailbox.tu-dresden.de Institut für Analysis, Technische Universität Dresden, Zellescher Weg 12-14, 01069 Dresden, Germany L. Perlich According to Arendt and

Journal

Complex Analysis and Operator TheorySpringer Journals

Published: Jun 5, 2018

References

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