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# Boundary triples for Schrodinger operators with singular interactions on hypersurfaces

- 1.0466591 - ÚJF 2017 RIV RU eng J - Journal Article
**Behrndt, J. - Langer, M. - Lotoreichik, Vladimir**

Boundary triples for Schrodinger operators with singular interactions on hypersurfaces.*Nanosystems: Physics, Chemistry, Mathematics*. Roč. 7, č. 2 (2016), s. 290-302. ISSN 2220-8054**R&D Projects**: GA ČR(CZ) GA14-06818S**Institutional support**: RVO:61389005**Keywords**: boundary triple * Weyl function * Schrodinger operator * singular potential * delta-interaction * hypersurface**Subject RIV**: BE - Theoretical Physics

The self-adjoint Schrodinger operator A(delta, alpha) with a delta-interaction of constant strength alpha supported on a compact smooth hypersurface C is viewed as a self-adjoint extension of a natural underlying symmetric operator S in L-2 (R-n). The aim of this note is to construct a boundary triple for S* and a self-adjoint parameter Theta(delta, alpha) in the boundary space L-2 (C) such that A(delta, alpha) corresponds to the boundary condition induced by Theta(delta, alpha). As a consequence, the well-developed theory of boundary triples and their Weyl functions can be applied. This leads, in particular, to a Krein-type resolvent formula and a description of the spectrum of A(delta, alpha) in terms of the Weyl function and Theta(delta, alpha).

**Permanent Link:**http://hdl.handle.net/11104/0264855

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