The fundamental equations for inversion of operator pencils on Banach space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:413

Article

Albrecht, Amie¹  Howlett, Phil¹  Pearce, Charles² 

[1] Univ S Australia, Ctr Ind & Appl Math, Scheduling & Control Grp, Mawson Lakes, SA 5095, Australia

[2] Univ Adelaide, Sch Math Sci, Adelaide, SA 5000, Australia

关键词: Operator pencil;    Resolvent;    Fundamental equations;    Singular perturbation;   

DOI  :  10.1016/j.jmaa.2013.11.060

来源: Elsevier

【 摘 要 】

We prove that the resolvent of a linear operator pencil, is analytic on an open annulus if and only if the coefficients of the Laurent series satisfy a system of fundamental equations and are geometrically bounded. Our analysis extends earlier work on the fundamental equations to include the case where the resolvent has an isolated essential singularity. We find a closed form for the resolvent and use the fundamental equations to establish key spectral separation properties when the resolvent has only a finite number of isolated singularities. Finally we show that our results can also be applied to polynomial pencils. Crown Copyright (C) 2013 Published by Elsevier Inc. All rights reserved.

【 授权许可】

Free