Jonathan Rohleder: The Dirichlet-to-Neumann operator and its connection to spectral theory

The Dirichlet-to-Neumann operator corresponding to an elliptic differential equation plays an important role in applications such as, e.g., electrical impedance tomography. In this talk we discuss its connection to the spectra of selfadjoint elliptic differential operators on bounded and unbounded Lipschitz domains. The presented results are multidimensional versions of known facts from Titchmarsh-Weyl theory for singular Sturm-Liouville operators on intervals.