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 firstname.lastname@example.org Institut für Analysis, Technische Universität Dresden, Zellescher Weg 12-14, 01069 Dresden, Germany L. Perlich According to Arendt and
Complex Analysis and Operator Theory – Springer Journals
Published: Jun 5, 2018
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