Non-self-adjoint graphs

Abstract

On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity transforms to self-adjoint Laplacians. Among other things, we describe a simple way how to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.

43 pages, 1 figure

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Cited by in corpus (10)

• Spectral enclosures for non-self-adjoint extensions of symmetric operators
• Spectrum of a non-selfadjoint quantum star graph
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• Complex magnetic fields: An improved Hardy-Laptev-Weidl inequality and quasi-self-adjointness
• Quantum graphs: self-adjoint, and yet exhibiting a nontrivial $\mathcal{P}\mathcal{T}$-symmetry
• Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions
• Laplacians with point interactions -- expected and unexpected spectral properties
• Quantum star-graph analogues of PT-symmetric square wells. II: Spectra
• Hidden symmetries in non-self-adjoint graphs
• Embedded trace operator for infinite metric trees