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We give a self-contained presentation of the theory of self-adjointextensions using the technique of boundary triples. A description of thespectra of self-adjoint extensions in terms of the corresponding Krein maps(Weyl functions) is given. Applications include quantum graphs, pointinteractions, hybrid spaces, singular perturbations.Comment: 81 pages, new references added, subsection 1.3 extended, typos  correcte

SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS