Inversion of perturbed linear operators that are singular at the origin

Phil Hewlett; Vladimir Ejov; Konstantin Avrachenkov

doi:10.1109/CDC.2003.1271900

Inversion of perturbed linear operators that are singular at the origin

Phil Hewlett
, Vladimir Ejov
, Konstantin Avrachenkov

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Citations (Scopus)

Abstract

We consider the inversion of perturbed linear operators on Hilbert space. Namely, we study linear operators that depend on a small parameter and are singular when the parameter is equal to zero. First we consider the af£ne dependence on the parameter. We treat subsequently the cases of bounded operators with closed range, bounded operators with non closed range, and densely defined and closed unbounded operators. Then, we extend the results to the cases of polynomial and analytic perturbations.

Original language	English
Title of host publication	42nd IEEE Conference on Decision and Control
Subtitle of host publication	Proceedings
Place of Publication	United States
Publisher	Institute of Electrical and Electronics Engineers
Pages	5628-5631
Number of pages	4
ISBN (Electronic)	0-7803-7925-X
ISBN (Print)	0-7803-7924-1
DOIs	https://doi.org/10.1109/CDC.2003.1271900
Publication status	Published - 15 Mar 2004
Externally published	Yes
Event	42nd IEEE Conference on Decision and Control - Maui, HI, United States Duration: 9 Dec 2003 → 12 Dec 2003

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2003
ISSN (Print)	0191-2216

Conference

Conference	42nd IEEE Conference on Decision and Control
Country/Territory	United States
City	Maui, HI
Period	9/12/03 → 12/12/03

Access to Document

10.1109/CDC.2003.1271900Licence: In Copyright

Cite this

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title = "Inversion of perturbed linear operators that are singular at the origin",

abstract = "We consider the inversion of perturbed linear operators on Hilbert space. Namely, we study linear operators that depend on a small parameter and are singular when the parameter is equal to zero. First we consider the af£ne dependence on the parameter. We treat subsequently the cases of bounded operators with closed range, bounded operators with non closed range, and densely defined and closed unbounded operators. Then, we extend the results to the cases of polynomial and analytic perturbations.",

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Hewlett, P, Ejov, V & Avrachenkov, K 2004, Inversion of perturbed linear operators that are singular at the origin. in 42nd IEEE Conference on Decision and Control: Proceedings. Proceedings of the IEEE Conference on Decision and Control, vol. 2003, Institute of Electrical and Electronics Engineers, United States, pp. 5628-5631, 42nd IEEE Conference on Decision and Control, Maui, HI, United States, 9/12/03. https://doi.org/10.1109/CDC.2003.1271900

Inversion of perturbed linear operators that are singular at the origin. / Hewlett, Phil; Ejov, Vladimir; Avrachenkov, Konstantin.
42nd IEEE Conference on Decision and Control: Proceedings. United States: Institute of Electrical and Electronics Engineers, 2004. p. 5628-5631 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2003).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Inversion of perturbed linear operators that are singular at the origin

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AU - Ejov, Vladimir

AU - Avrachenkov, Konstantin

PY - 2004/3/15

Y1 - 2004/3/15

N2 - We consider the inversion of perturbed linear operators on Hilbert space. Namely, we study linear operators that depend on a small parameter and are singular when the parameter is equal to zero. First we consider the af£ne dependence on the parameter. We treat subsequently the cases of bounded operators with closed range, bounded operators with non closed range, and densely defined and closed unbounded operators. Then, we extend the results to the cases of polynomial and analytic perturbations.

AB - We consider the inversion of perturbed linear operators on Hilbert space. Namely, we study linear operators that depend on a small parameter and are singular when the parameter is equal to zero. First we consider the af£ne dependence on the parameter. We treat subsequently the cases of bounded operators with closed range, bounded operators with non closed range, and densely defined and closed unbounded operators. Then, we extend the results to the cases of polynomial and analytic perturbations.

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DO - 10.1109/CDC.2003.1271900

M3 - Conference contribution

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T3 - Proceedings of the IEEE Conference on Decision and Control

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T2 - 42nd IEEE Conference on Decision and Control

Y2 - 9 December 2003 through 12 December 2003

ER -

Inversion of perturbed linear operators that are singular at the origin

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