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.doi-10_2478_v10062-012-0004-2,
author = {Michael Gil},
title = {Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space},
journal = {Annales UMCS, Mathematica},
volume = {66},
year = {2012},
pages = {25-39},
zbl = {1270.34167},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0004-2}
}
Michael Gil. Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space. Annales UMCS, Mathematica, Tome 66 (2012) pp. 25-39. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0004-2/
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