### Abstract

Let Σ⊂ℝ

^{d}be a C^{∞}-smooth closed compact hypersurface, which splits the Euclidean space ℝ^{d}into two domains Ω_{±}. In this note self-adjoint Schrödinger operators with δ and δ'-interactions supported on Σ are studied. For large enough*m*∈ℕ the difference of*m*th powers of resolvents of such a Schrödinger 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 L^{2}(ℝ^{d}) is written in terms of Neumann-to-Dirichlet maps on the boundary space L^{2}(Σ).Original language | English |
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Title of host publication | Functional Analysis and Operator Theory for Quantum Physics |

Subtitle of host publication | The Pavel Exner Anniversary Volume |

Editors | Jaroslav Dittrich, Hynek Kovarik, Ari Laptev |

Place of Publication | Switzerland |

Pages | 129-152 |

Number of pages | 24 |

ISBN (Electronic) | 9783037196755 |

DOIs | |

Publication status | Published - 31 May 2017 |

### Publication series

Name | EMS Series of Congress Reports |
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Publisher | European Mathematical Society |

Volume | 12 |

### Keywords

- trace formula
- delta interaction
- Schroedinger operator
- singular potential

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## Cite this

Behrndt, J., Langer, M., & Lotoreichik, V. (2017). Trace formulae for Schrödinger operators with singular interactions. In J. Dittrich, H. Kovarik, & A. Laptev (Eds.),

*Functional Analysis and Operator Theory for Quantum Physics: The Pavel Exner Anniversary Volume*(pp. 129-152). (EMS Series of Congress Reports; Vol. 12). Switzerland. https://doi.org/10.4171/175-1/6