Bounds on the non-real spectrum of differential operators with indefinite weights

Behrndt, Jussi GND; Philipp, Friedrich; Trunk, Carsten GND

Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein spaces. Under the assumption that 0 and infinity are not singular critical points of the unperturbed operator it is shown that a bounded additive perturbation leads to an operator whose non-real spectrum is contained in a compact set and with definite type real spectrum outside this set. The main results are quantitative estimates for this set, which are applied to Sturm-Liouville and second order elliptic partial differential operators with indefinite weights on unbounded domains.

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Behrndt Univ.-Prof. Dr., J., Philipp Dr., F., Trunk Univ.-Prof. Dr. rer. nat. habil., C., 2012. Bounds on the non-real spectrum of differential operators with indefinite weights. Preprint /  Technische Universität Ilmenau, Institut für Mathematik, Preprint /  Technische Universität Ilmenau, Institut für Mathematik 12–07.
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