A spectral shift function for Schröodinger operators with singular interactions

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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.

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Behrndt, J., Gesztesy, F., & Nakamura, S. (2018). A spectral shift function for Schröodinger operators with singular interactions. In Operator Theory: Advances and Applications (Vol. 268, pp. 89–110). Springer International Publishing. https://doi.org/10.1007/978-3-319-75996-8_4

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