Mathematical Physics Seminar

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.