We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.
@article{bwmeta1.element.ojs-doi-10_17951_a_2012_66_1_25-39,
author = {Michael Gil'},
title = {Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {66},
year = {2012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2012_66_1_25-39}
}
Michael Gil’. Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 66 (2012) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2012_66_1_25-39/
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