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Boundary value problems for adjoint pairs of operators
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abstract
The notion of quasi boundary triples and their Weyl functions from extension theory of symmetric operators is extended to the general framework of adjoint pairs of operators under minimal conditions on the boundary maps. With the help of the corresponding abstract Titchmarsh-Weyl $M$-functions sufficient conditions for the unique solvability of the related boundary value problems are obtained and the solutions are expressed via Krein-type resolvent formulae. The abstract theory developed in this manuscript can be applied to a large class of elliptic differential operators.
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Generalized boundary triples for adjoint pairs with applications to non-self-adjoint Schr\"odinger operators
Robin realizations of Schrödinger operators with complex L^p potentials on Lipschitz domains are closed and have a nonempty resolvent set, via generalized boundary triples for adjoint pairs.
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