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Spectral analysis of rank one perturbations and applications. (English) Zbl 0824.47019
Feldman, J. (ed.) et al., Mathematical quantum theory II: Schrödinger operators. Proceedings of the Canadian Mathematical Society annual seminar on mathematical quantum theory held in Vancouver, Canada, August 4-14, 1993. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 8, 109-149 (1995).
Summary: A review of the general theory of selfadjoint operators of the form $$A+ \alpha B$$, where $$B$$ is rank one is presented. Applications include proofs of localization for Schrödinger operators, results on inverse spectral theory, and examples of operators with singular continuous spectrum.
For the entire collection see [Zbl 0815.00011].

##### MSC:
 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.) 47A10 Spectrum, resolvent 47A55 Perturbation theory of linear operators 34L05 General spectral theory of ordinary differential operators 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 34F05 Ordinary differential equations and systems with randomness