A spectral shift function for Schröodinger operators with singular interactions

Abstract

For the pair ˆ’Δ, ˆ’Δ ˆ’αδC of self-adjoint Schröodinger operators in L2(ℝn) a spectral shift function is determined in an explicit form with the help of (energy parameter dependent) Dirichlet-to-Neumann maps. Here δC denotes a singular δ-potential which is supported on asmooth compact hypersurface C ⊂ (ℝn) and δ is a real-valued function on C.