Boundary triples for Schrödinger operators with singular interactions on hypersurfaces
Jussi BehrndtInstitut fr Numerische Mathematik, Technische Universitt Graz, Steyrergasse 30, 8010 Graz, AustriaMatthias LangerDepartment of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, United KingdomVladimir LotoreichikDepartment of Theoretical Physics, Nuclear Physics Institute CAS, 250 68 e near Prague, Czech Republic
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Abstract
The self-adjoint Schrdinger operator A , with a -interaction of constant strength 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 , in the boundary space L 2 (C) such that A , corresponds to the boundary condition induced by , . 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 , in terms of the Weyl function and , .
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