@inbook{81b045854f77456fa6cfddcb9a00ee45,

title = "Trace formulae for Schr{\"o}dinger operators with singular interactions",

abstract = "Let Σ⊂ℝd be a C∞-smooth closed compact hypersurface, which splits the Euclidean space ℝd into two domains Ω±. In this note self-adjoint Schr{\"o}dinger operators with δ and δ'-interactions supported on Σ are studied. For large enough m∈ℕ the difference of mth powers of resolvents of such a Schr{\"o}dinger operator and the free Laplacian is known to belong to the trace class. We prove trace formulae, in which the trace of the resolvent power difference in L2(ℝd) is written in terms of Neumann-to-Dirichlet maps on the boundary space L2(Σ). ",

keywords = "trace formula, delta interaction, Schroedinger operator, singular potential",

author = "Jussi Behrndt and Matthias Langer and Vladimir Lotoreichik",

year = "2017",

month = may,

day = "31",

doi = "10.4171/175-1/6",

language = "English",

isbn = "9783037191750",

series = "EMS Series of Congress Reports",

publisher = "European Mathematical Society",

pages = "129--152",

editor = "Jaroslav Dittrich and Hynek Kovarik and Ari Laptev",

booktitle = "Functional Analysis and Operator Theory for Quantum Physics",

}