On the point spectrum of some perturbed differential operators with periodic coefficients

Details On the point spectrum of some perturbed differential operators with periodic coefficients On the point spectrum of some perturbed differential operators with periodic coefficients

2007-08-06

arxiv.org/abs/0708.0854v1

Mathematics

Spectral Theory

Scientific paper

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.

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