Inversion of analytically perturbed linear operators that are singular at the origin

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:353

Article

Howlett, Phil²  Avrachenkov, Konstantin³  Pearce, Charles¹  Ejov, Vladimir² 

[1] Univ Adelaide, Sch Math Sci, Adelaide, SA, Australia

[2] Univ S Australia, Ctr Ind & Appl Math, Mawson Lakes, Australia

[3] INRIA, Sophia Antipolis, France

关键词: Linear operator;    Analytic perturbation;    Inverse operator;   

DOI  :  10.1016/j.jmaa.2008.11.074

来源: Elsevier

【 摘 要 】

Let H and K be Hilbert spaces and for each z is an element of C let A(Z) is an element of L(H, K) be a bounded but not necessarily compact linear map with A(z) analytic on a region |z| < a. If A(0) is singular we find conditions under which A(z)(-1) is well defined on some region 0 < |z| < b by a convergent Laurent series with a finite order pole at the origin. We show that by changing to a standard Sobolev topology the method extends to closed unbounded linear operators and also that it can be used in Banach spaces where complementation of certain closed subspaces is possible. Our method is illustrated with several key examples. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free