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

2025/05/28 by Arnal, Antonio, Behrndt, Jussi, Holzmann, Markus +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2505.22321

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.

Citations

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Cited by

• Approximation of magnetic Schrödinger operators with δ-interactions supported on networks

Related

• Boundary value problems for adjoint pairs of operators
• Boundary triples and Weyl functions for singular perturbations of self-adjoint operators
• Quasi boundary triples, self-adjoint extensions, and Robin Laplacians on the half-space
• Generalized boundary triples, Weyl functions and inverse problems
• Boundary triplets and M -functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices