Coupling of symmetric operators and the third Green identity

Abstract

The principal aim of this paper is to derive an abstract form of the third Green identity associated with a proper extension $T$ of a symmetric operator $S$ in a Hilbert space $\mathfrak{H}$, employing the technique of quasi boundary triples for $T$. The general results are illustrated with couplings of Schrödinger operators on Lipschitz domains on smooth, boundaryless Riemannian manifolds.

26 pages