Download PT-Symmetric Schrödinger Operators with Unbounded Potentials by Jan Nesemann PDF

By Jan Nesemann

Following the pioneering paintings of Carl. M. Bender et al, (1998), there was an expanding curiosity in theoretical physics in so-called PT-symmetric Schrödinger operators. within the actual literature, the life of Schrödinger operators with PT-symmetric complicated potentials having actual spectrum was once thought of a shock and lots of examples of such potentials have been studied within the sequel. From a mathematical viewpoint, despite the fact that, this can be no shock in any respect - delivering one is aware the idea of self-adjoint operators in Krein areas. Jan Nesemann experiences really bounded perturbations of self-adjoint operators in Krein areas with genuine spectrum. the most effects offer stipulations which warrantly the spectrum of the perturbed operator to stay actual. comparable effects are validated for quite form-bounded perturbations and for pseudo-Friedrichs extensions. the writer will pay specific recognition to the case while the unperturbed self-adjoint operator has infinitely many spectral gaps, both among eigenvalues, or extra normally, among separated components of the spectrum.

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