Spectral theory for structured perturbations of linear operators

2016/06/16 by Martin Adler, Adler, Martin, Klaus-Jochen Engel +1
Mathematics · #47A10 #47A55 #FOS: Mathematics #Spectral Theory (math.SP) #math.SP #msc:47A10 #msc:47A55

paper · pdf · doi:10.48550/arxiv.1606.05205

arxiv created 2016/06/16 · arxiv updated 2016/10/05

Abstract

We characterize the spectrum (and its parts) of operators which can be represented as G=A+BC for a simpler operator A and a structured perturbation BC. The interest in this kind of perturbations is motivated, e.g., by perturbations of the domain of an operator A but also arises in the theory of closed-loop systems in control theory. In many cases our results yield the spectral values of G as zeros of a "characteristic equation".

Related

• A brief overview of spectral perturbation Theory
• Removal of the resolvent-like dependence on the spectral parameter from perturbations
• Spectral Methods in Complex Systems
• Direct and inverse spectral problems for rank-one perturbations of self-adjoint operators
• Non-symmetric perturbations of self-adjoint operators