On the point spectrum of nonselfadjoint operators
by
Igor Cialenco
Moldova State University

The problem of the finiteness of the point spectrum of some classes of nonselfadjoint operators are investigated. In particular, the perturbations of Wiener-Hopf type operators, the operators generated by Jacobi matrices, the differential operators (generally, for superior order) and other classes of operators are studied. The main results are obtained using direct methods of the theory of perturbations of spectrum of linear operators. Sufficient conditions for existence of holomorphic extension of the resolvent of the unperturbed operator through its continuous spectrum are established which imply the finiteness of the point spectrum (more exactly, of the set of spectral singularities ) of the perturbed operator. The main results are in concordance with those established before by many authors (see, for instance, , ).

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M.A.Naimark, Linear differential operators, Moskva, Nauka, 1954.

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V.Ljance, A nonselfadjoint difference operator, Dokl. Akad. Nauk S.S.S.R., 173, N6, 1967, p.1260-1263.

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B.P.Pavlov, On a nonselfadjoint Schrödinger Operator, Problems of Mathematics Physics 1, Izdat. Leningrad. Univer., 1996, p.102-132.

Date received: May 29, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeo-35.