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Bounds on the non-real spectrum of differential operators with indefinite weights. (English) Zbl 1281.47024

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.

MSC:

47B50 Linear operators on spaces with an indefinite metric
47A55 Perturbation theory of linear operators
34B24 Sturm-Liouville theory
47E05 General theory of ordinary differential operators
47F05 General theory of partial differential operators
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
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References:

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