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Bounds on the Non-real Spectrum of Differential Operators with Indefinite Weights

Jussi BehrndtFriedrich PhilippCarsten Trunk

出版	Techn. Univ., Inst. für Mathematik, 2012
URL	http://books.google.com.hk/books?id=g3YGyAEACAAJ&hl=&source=gbs_api

註釋

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.