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Weyl function and spectral properties of self-adjoint extensions

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Abstract

We characterize the spectra of self-adjoint extensions of a symmetric operator with equal deficiency indices in terms of boundary values of their Weyl functions. A complete description is obtained for the point and absolutely continuous spectrum while for the singular continuous spectrum additional assumptions are needed. The results are illustrated by examples.

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Brasche, J.F., Malamud, M. & Neidhardt, H. Weyl function and spectral properties of self-adjoint extensions. Integr equ oper theory 43, 264–289 (2002). https://doi.org/10.1007/BF01255563

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