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 -