Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/50622
Citations | ||
Scopus | Web of Science® | Altmetric |
---|---|---|
?
|
?
|
Type: | Journal article |
Title: | Inversion of analytically perturbed linear operators that are singular at the origin |
Author: | Howlett, P. Avrachenkov, K. Pearce, C. Ejov, V. |
Citation: | Journal of Mathematical Analysis and Applications, 2009; 353(1):68-84 |
Publisher: | Academic Press Inc Elsevier Science |
Issue Date: | 2009 |
ISSN: | 0022-247X 1096-0813 |
Statement of Responsibility: | Phil Howlett, Konstantin Avrachenkov, Charles Pearce, and Vladimir Ejova |
Abstract: | Let H and K be Hilbert spaces and for each z ∈ C let A (z) ∈ 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.22This paper is based on preliminary work in [P.G. Howlett, K.E. Avrachenkov, Laurent series for the inversion of perturbed lionear operators on Hilbert space, in: A. Rubinov (Ed.), Progress in Optimisation III, Contributions from Australasia, Kluwer, 2001, pp. 325-342; P.G. Howlett, V. Ejov, K.E. Avrachenkov, Inversion of perturbed linear operators that are singular at the origin, in: Proceedings of 42nd IEEE Conference on Decision and Control, Maui, Hawai, December 2003, pp. 5628-5631 (on compact disc)]. © 2008 Elsevier Inc. All rights reserved. |
Keywords: | Linear operator Analytic perturbation Inverse operator |
Description: | Copyright © 2008 Elsevier Inc. All rights reserved. |
DOI: | 10.1016/j.jmaa.2008.11.074 |
Published version: | http://dx.doi.org/10.1016/j.jmaa.2008.11.074 |
Appears in Collections: | Aurora harvest Mathematical Sciences publications |
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.