IJPAM: Volume 50, No. 1 (2009)

ON THE POINT SPECTRUM OF SOME PERTURBED
DIFFERENTIAL OPERATORS WITH PERIODIC COEFFICIENTS

Igor Cialenco
Department of Applied Mathematics
Illinois Institute of Technology
30W, 32-nd Str., E1 234C, Chicago, IL 60616-3793, USA
e-mail: [email protected]


Abstract.Finiteness of the point spectrum of linear operators acting in a Banach space is investigated from point of view of perturbation theory. In the first part of the paper we present an abstract result based on analytical continuation of the resolvent function through continuous spectrum. In the second part, the abstract result is applied to differential operators which can be represented as a differential operator with periodic coefficients perturbed by an arbitrary subordinated differential operator.

Received: October 21, 2008

AMS Subject Classification: 47A10, 47A55, 47A75, 47E05, 34L10

Key Words and Phrases: spectral theory, perturbation theory, point spectrum, differential operators, nonselfadjoint operators

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 1