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August  2017, 10(4): 661-671. doi: 10.3934/dcdss.2017033

## The Dirichlet-to-Neumann map for Schrödinger operators with complex potentials

 1 Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria 2 Department of Mathematics, University of Auckland, Private bag 92019, Auckland 1142, New Zealand

* Corresponding author: A.F.M ter Elst

Received  June 2016 Revised  December 2016 Published  April 2017

Let $\Omega \subset \mathbb{R}^d$ be a bounded open set with Lipschitz boundary and let $q \colon \Omega \to \mathbb{C}$ be a bounded complex potential. We study the Dirichlet-to-Neumann graph associated with the operator $- \Delta + q$ and we give an example in which it is not $m$-sectorial.

Citation: Jussi Behrndt, A. F. M. ter Elst. The Dirichlet-to-Neumann map for Schrödinger operators with complex potentials. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 661-671. doi: 10.3934/dcdss.2017033
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