Generalized boundary triples for adjoint pairs with applications to non-self-adjoint Schrödinger operators
Preprint
Abstract
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.Keywords
All Related Versions
This publication has 41 references indexed in Scilit:
- Generalized boundary triples, II. Some applications of generalized boundary triples and form domain invariant Nevanlinna functionsMathematische Nachrichten, 2022
- Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functionsMathematische Nachrichten, 2020
- Quasi Boundary Triples, Self-adjoint Extensions, and Robin Laplacians on the Half-space2019
- Boundary pairs associated with quadratic formsMathematische Nachrichten, 2015
- The Abstract Titchmarsh-Weyl M-function for Adjoint Operator Pairs and its Relation to the SpectrumIntegral Equations and Operator Theory, 2009
- M ‐functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problemsMathematische Nachrichten, 2009
- Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schrödinger Operators on Bounded Lipschitz Domains2009
- The Inhomogeneous Dirichlet Problem in Lipschitz DomainsJournal of Functional Analysis, 1995
- The extension theory of Hermitian operators and the moment problemJournal of Mathematical Sciences, 1995
- Extensions of closed operators in Hilbert spaceMathematical Notes, 1980