Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space

Michael Gil’

Abstract


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.

Keywords


Abstract differential operator; spectrum; resolvent, stability; instability

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References


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DOI: http://dx.doi.org/10.2478/v10062-012-0004-2
Date of publication: 2016-07-24 20:22:24
Date of submission: 2016-07-24 15:49:17


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