Coupling of symmetric operators and the third Green identity

preprint2016arXivOpen access

Abstract

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

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