Complex Anal. Oper. Theory
and Operator Theory
Dirichlet-to-Robin Operators via Composition
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
Keywords Composition operators · Spaces of holomorphic functions ·
Dirichlet-to-Neumann · Dirichlet-to-Robin
Mathematics Subject Classiﬁcation 47B38 · 47B33 · 47D06
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.
Institut für Analysis, Technische Universität Dresden, Zellescher Weg 12-14, 01069 Dresden,