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

2007/08/06 by Igor Cialenco, Cialenco, Igor
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Spectral Theory in Mathematical Physics #math.FA #math.SP #msc:34L10 #msc:47A10 #msc:47A55 #msc:47A75 #msc:47E05

paper · pdf · doi:10.48550/arxiv.0708.0854

arxiv created 2007/08/06 · arxiv updated 2009/12/01

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.

Related

• On the Spectrality of the Differential Operators with Periodic Coefficients
• Absence of eigenvalues for integro-differential operators with periodic coefficients
• On spectrum of a periodic operator with a small localized perturbation
• Eigenvalue problems for Fredholm operators with set-valued perturbations
• Spectral theory for structured perturbations of linear operators