Boundary triples for Schrödinger operators with singular interactions on hypersurfaces

The self-adjoint Schrödinger operator A_δ,α with a δ-interaction of constant strength α supported on a compact smooth hypersurface C is viewed as a self-adjoint extension of a natural underlying symmetric operator S in L²(ℝⁿ). The aim of this note is to construct a boundary triple for S* and a self-adjoint parameter Θ_δ,α in the boundary space L²(C) such that A_δ,α corresponds to the boundary condition induced by Θ_δ,α. 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_δ,α in terms of the Weyl function and Θ_δ,α.