TY - JOUR

T1 - Boundary triples for Schrödinger operators with singular interactions on hypersurfaces

AU - Behrndt, Jussi

AU - Langer, Matthias

AU - Lotoreichik, Vladimir

PY - 2016

Y1 - 2016

N2 - he 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).

AB - he 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).

U2 - 10.17586/2220-8054-2016-7-2-290-302

DO - 10.17586/2220-8054-2016-7-2-290-302

M3 - Article

SN - 2220-8054

VL - 7

SP - 290

EP - 302

JO - Nanosystems: Physics, Chemistry, Mathematics

JF - Nanosystems: Physics, Chemistry, Mathematics

IS - 2

ER -