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

Identifieur interne : 002E58 ( PascalFrancis/Corpus ); précédent : 002E57; suivant : 002E59

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

Auteurs : Phil Howlett ; Konstantin Avrachenkov ; Charles Pearce ; Vladimir Ejov

Source :

RBID : Pascal:09-0188915

Descripteurs français

English descriptors

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| -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.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

pA  
A01 01  1    @0 0022-247X
A02 01      @0 JMANAK
A03   1    @0 J. math. anal. appl.
A05       @2 353
A06       @2 1
A08 01  1  ENG  @1 Inversion of analytically perturbed linear operators that are singular at the origin
A11 01  1    @1 HOWLETT (Phil)
A11 02  1    @1 AVRACHENKOV (Konstantin)
A11 03  1    @1 PEARCE (Charles)
A11 04  1    @1 EJOV (Vladimir)
A14 01      @1 Centre for Industrial and Applied Mathematics, University of South Australia @2 Mawson Lakes @3 AUS @Z 1 aut. @Z 4 aut.
A14 02      @1 INRIA @2 Sophia Antipoles @3 FRA @Z 2 aut.
A14 03      @1 School of Mathematical Sciences, University of Adelaide @2 Adelaide @3 AUS @Z 3 aut.
A20       @1 68-84
A21       @1 2009
A23 01      @0 ENG
A43 01      @1 INIST @2 2980 @5 354000186800260080
A44       @0 0000 @1 © 2009 INIST-CNRS. All rights reserved.
A45       @0 23 ref.
A47 01  1    @0 09-0188915
A60       @1 P
A61       @0 A
A64 01  1    @0 Journal of mathematical analysis and applications
A66 01      @0 USA
C01 01    ENG  @0 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.
C02 01  X    @0 001A02E17
C02 02  X    @0 001A02E16
C03 01  X  FRE  @0 Opérateur linéaire @5 17
C03 01  X  ENG  @0 Linear operator @5 17
C03 01  X  SPA  @0 Operador lineal @5 17
C03 02  X  FRE  @0 Espace Hilbert @5 18
C03 02  X  ENG  @0 Hilbert space @5 18
C03 02  X  SPA  @0 Espacio Hilbert @5 18
C03 03  X  FRE  @0 Espace Banach @5 19
C03 03  X  ENG  @0 Banach space @5 19
C03 03  X  SPA  @0 Espacio Banach @5 19
C03 04  X  FRE  @0 Perturbation @5 20
C03 04  X  ENG  @0 Perturbation @5 20
C03 04  X  SPA  @0 Perturbación @5 20
C03 05  X  FRE  @0 Application @5 21
C03 05  X  ENG  @0 Application @5 21
C03 05  X  SPA  @0 Aplicación @5 21
C03 06  X  FRE  @0 Analyse mathématique @5 22
C03 06  X  ENG  @0 Mathematical analysis @5 22
C03 06  X  SPA  @0 Análisis matemático @5 22
C03 07  X  FRE  @0 47Axx @4 INC @5 70
C03 08  X  FRE  @0 46Cxx @4 INC @5 71
C03 09  X  FRE  @0 46Bxx @4 INC @5 72
C03 10  X  FRE  @0 46C07 @4 INC @5 73
C03 11  X  FRE  @0 Sous espace @4 INC @5 74
C03 12  X  FRE  @0 Opérateur inverse @4 INC @5 75
N21       @1 138
N44 01      @1 OTO
N82       @1 OTO

Format Inist (serveur)

NO : PASCAL 09-0188915 INIST
ET : Inversion of analytically perturbed linear operators that are singular at the origin
AU : HOWLETT (Phil); AVRACHENKOV (Konstantin); PEARCE (Charles); EJOV (Vladimir)
AF : Centre for Industrial and Applied Mathematics, University of South Australia/Mawson Lakes/Australie (1 aut., 4 aut.); INRIA/Sophia Antipoles/France (2 aut.); School of Mathematical Sciences, University of Adelaide/Adelaide/Australie (3 aut.)
DT : Publication en série; Niveau analytique
SO : Journal of mathematical analysis and applications; ISSN 0022-247X; Coden JMANAK; Etats-Unis; Da. 2009; Vol. 353; No. 1; Pp. 68-84; Bibl. 23 ref.
LA : Anglais
EA : 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.
CC : 001A02E17; 001A02E16
FD : Opérateur linéaire; Espace Hilbert; Espace Banach; Perturbation; Application; Analyse mathématique; 47Axx; 46Cxx; 46Bxx; 46C07; Sous espace; Opérateur inverse
ED : Linear operator; Hilbert space; Banach space; Perturbation; Application; Mathematical analysis
SD : Operador lineal; Espacio Hilbert; Espacio Banach; Perturbación; Aplicación; Análisis matemático
LO : INIST-2980.354000186800260080
ID : 09-0188915

Links to Exploration step

Pascal:09-0188915

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