Spectra of self-adjoint extensions and applications to solvable Schroedinger operators

Abstract

We give a self-contained presentation of the theory of self-adjoint extensions using the technique of boundary triples. A description of the spectra of self-adjoint extensions in terms of the corresponding Krein maps (Weyl functions) is given. Applications include quantum graphs, point interactions, hybrid spaces, singular perturbations.

81 pages, new references added, subsection 1.3 extended, typos corrected

References in corpus (7)

• Quantum wires with magnetic fluxes
• Boundary triples and Weyl functions for singular perturbations of self-adjoint operators
• Large gaps in point-coupled periodic systems of manifolds
• A remark on Krein's resolvent formula and boundary conditions
• Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction
• Absolute continuity in periodic thin tubes and strongly coupled leaky wires
• On-diagonal singularities of the Green functions for Schroedinger operators

Cited by in corpus (10)

• First order operators and boundary triples
• Equilateral quantum graphs and boundary triples
• M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems
• Spectral analysis of metric graphs and related spaces
• Localization on quantum graphs with random edge lengths
• Localization on quantum graphs with random vertex couplings
• Spectral Analysis of a Two Body Problem with Zero Range Perturbation
• Self-adjoint Extensions of Restrictions
• Quasiperiodic surface Maryland models on quantum graphs
• Eigenvalue bracketing for discrete and metric graphs