Spectral analysis of rank one perturbations and applications. (English) Zbl 0824.47019

Simon, Barry

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

Keywords:

selfadjoint operators; localization for Schrödinger operators; inverse spectral theory; operators with singular continuous spectrum