Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 472

Weyl function and spectral properties of self-adjoint extensions

J. F. Brasche, M. M. Malamud, H. Neidhardt

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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