A spectral shift function for Schröodinger operators with singular interactions

Abstract.

For the pair $-\Delta,-\Delta-\alpha\delta_\mathcal{C}$ of self-adjoint Schröodinger operators in $L^2(\mathbb{R}^n)$ a spectral shift function is determined in an explicit form with the help of (energy parameter dependent) Dirichlet-to-Neumann maps. Here δ_C denotes a singular δ-potential which is supported on a smooth compact hypersurface ${ C}\subset(\mathbb{R}^n)$ and δ is a real-valued function on C.