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Spectral analysis of polynomial operator pencils with continuously pointwise spectrum. (Russian. English summary) Zbl 0643.47012

The present paper deals with a spectral analysis of perturbed non- selfadjoint polynomial pencils in a Hilbert space. The structure and location of the spectrum in the complex plane are investigated. Sufficient conditions have been obtained under which the resolvent can be extended finite-meromorphically to the continuous spectrum. The principal part of the resolvent is expressed in terms of generalized eigen and adjoint vectors in the neighbourhood of generalized eigenvalues. A theorem on multiple expansion in terms of generalized eigen and adjoint vectors is obtained.
Reviewer: P.C.Sinha

MSC:

47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
47A55 Perturbation theory of linear operators
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
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