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arXiv · 1204.1112

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

Jussi Behrndt·Friedrich Philipp·Carsten Trunk
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Abstract

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 $\infty$ 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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Jussi Behrndt, Friedrich Philipp, Carsten Trunk. 2012-04-05. Bounds on the non-real spectrum of differential operators with indefinite weights. https://arxiv.org/abs/1204.1112

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