Generalized boundary triples for adjoint pairs with applications to non-self-adjoint Schrödinger operators

We extend the notion of generalized boundary triples and their Weyl functions from extension theory of symmetric operators to adjoint pairs of operators, and we provide criteria on the boundary parameters to induce closed operators with a nonempty resolvent set. The abstract results are applied to Schrödinger operators with complex $L^p$-potentials on bounded and unbounded Lipschitz domains with compact boundaries.