Maksudov, F. G.; Allakhverdiev, B. P. Spectral analysis of polynomial operator pencils with continuously pointwise spectrum. (Russian. English summary) Zbl 0643.47012 Dokl., Akad. Nauk Az. SSR 43, No. 1, 3-7 (1987). 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 Keywords:spectral analysis of perturbed non-selfadjoint polynomial pencils in a Hilbert space; structure and location of the spectrum; continuous spectrum; generalized eigen and adjoint vectors; multiple expansion in terms of generalized eigen and adjoint vectors PDFBibTeX XMLCite \textit{F. G. Maksudov} and \textit{B. P. Allakhverdiev}, Dokl., Akad. Nauk Az. SSR 43, No. 1, 3--7 (1987; Zbl 0643.47012)