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Wednesday, November 02, 2016
12:00 PM - 1:00 PM

Mathematical Physics Seminar

Spectral shift functions and Dirichlet-to-Neumann maps
Jussi Behrndt, Institut für Numerische Mathematik, Technische Universität Graz,

In this talk we discuss a representation formula for the spectral shift function of a pair of self-adjoint operators via an abstract operator valued Titchmarsh-Weyl m-function. The general result is applied to different self-adjoint realizations of second-order elliptic partial differential operators on smooth domains with compact boundaries, Schrödinger operators with compactly supported potentials, and finally, Schrödinger operators with singular potentials supported on hypersurfaces. n these applications the spectral shift function is determined in an explicit form with the help of (energy parameter dependent) Dirichlet-to-Neumann maps. The talk is based on joint work with Fritz Gesztesy and Shu Nakamura.

For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].