Mathematics – Spectral Theory
Scientific paper
2012-04-05
Mathematics
Spectral Theory
27 pages
Scientific paper
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.
Behrndt Jussi
Philipp Friedrich
Trunk Carsten
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