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TRACE IDENTITIES FOR COMMUTATORS, WITH APPLICATIONS TO THE DISTRIBUTION OF EIGENVALUES

Identifieur interne : 000065 ( PascalFrancis/Curation ); précédent : 000064; suivant : 000066

TRACE IDENTITIES FOR COMMUTATORS, WITH APPLICATIONS TO THE DISTRIBUTION OF EIGENVALUES

Auteurs : Evans M. Ii Harrell [États-Unis] ; Joachim Stubbe [Suisse]

Source :

RBID : Pascal:11-0490120

Descripteurs français

English descriptors

Abstract

We prove trace identities for commutators of operators, which are used to derive sum rules and sharp universal bounds for the eigenvalues of periodic Schrödinger operators and Schrödinger operators on immersed manifolds. In particular, we prove bounds on the eigenvalue λN+1 in terms of the lower spectrum, bounds on ratios of means of eigenvalues, and universal monotonicity properties of eigenvalue moments, which imply sharp versions of Lieb-Thirring inequalities. In the case of a Schrödinger operator on an immersed manifold of dimension d, we derive a version of Reilly's inequality bounding the eigenvalue λN+1 of the Laplace-Beltrami operator by a universal constant times ⁄h⁄2∞N2/d.
pA  
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A06       @2 12
A08 01  1  ENG  @1 TRACE IDENTITIES FOR COMMUTATORS, WITH APPLICATIONS TO THE DISTRIBUTION OF EIGENVALUES
A11 01  1    @1 HARRELL (Evans M. II)
A11 02  1    @1 STUBBE (Joachim)
A14 01      @1 SCHOOL OF MATHEMATICS, GEORGIA INSTITUTE OF TECHNOLOGY @2 ATLANTA, GEORGIA 30332-0610 @3 USA @Z 1 aut.
A14 02      @1 DEPARTMENT OF MATHEMATICS, ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE, IMB-FSB, STATION 8 @2 1015 LAUSANNE @3 CHE @Z 2 aut.
A20       @1 6385-6405
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A44       @0 0000 @1 © 2011 INIST-CNRS. All rights reserved.
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C01 01    ENG  @0 We prove trace identities for commutators of operators, which are used to derive sum rules and sharp universal bounds for the eigenvalues of periodic Schrödinger operators and Schrödinger operators on immersed manifolds. In particular, we prove bounds on the eigenvalue λN+1 in terms of the lower spectrum, bounds on ratios of means of eigenvalues, and universal monotonicity properties of eigenvalue moments, which imply sharp versions of Lieb-Thirring inequalities. In the case of a Schrödinger operator on an immersed manifold of dimension d, we derive a version of Reilly's inequality bounding the eigenvalue λN+1 of the Laplace-Beltrami operator by a universal constant times ⁄h⁄2∞N2/d.
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C03 01  X  FRE  @0 Trace @5 17
C03 01  X  ENG  @0 Trace @5 17
C03 01  X  SPA  @0 Traza @5 17
C03 02  X  FRE  @0 Distribution @5 18
C03 02  X  ENG  @0 Distribution @5 18
C03 02  X  SPA  @0 Distribución @5 18
C03 03  X  FRE  @0 Fonction répartition @5 19
C03 03  X  ENG  @0 Distribution function @5 19
C03 03  X  SPA  @0 Función distribución @5 19
C03 04  X  FRE  @0 Valeur propre @5 20
C03 04  X  ENG  @0 Eigenvalue @5 20
C03 04  X  SPA  @0 Valor propio @5 20
C03 05  X  FRE  @0 Règle somme @5 21
C03 05  X  ENG  @0 Sum rule @5 21
C03 05  X  SPA  @0 Regla suma @5 21
C03 06  X  FRE  @0 Opérateur Schrödinger @5 22
C03 06  X  ENG  @0 Schrödinger operator @5 22
C03 06  X  SPA  @0 Operador Schrodinger @5 22
C03 07  X  FRE  @0 Variété mathématique @5 23
C03 07  X  ENG  @0 Manifold @5 23
C03 07  X  SPA  @0 Variedad matemática @5 23
C03 08  X  FRE  @0 Borne inférieure @5 24
C03 08  X  ENG  @0 Lower bound @5 24
C03 08  X  SPA  @0 Cota inferior @5 24
C03 09  X  FRE  @0 Monotonie @5 25
C03 09  X  ENG  @0 Monotonicity @5 25
C03 09  X  SPA  @0 Monotonía @5 25
C03 10  X  FRE  @0 Moment statistique @5 26
C03 10  X  ENG  @0 Statistical moment @5 26
C03 10  X  SPA  @0 Momento estadístico @5 26
C03 11  X  FRE  @0 60E05 @4 INC @5 70
C03 12  X  FRE  @0 65F15 @4 INC @5 71
C03 13  X  FRE  @0 65H17 @4 INC @5 72
C03 14  X  FRE  @0 Opérateur périodique @4 INC @5 73
C03 15  X  FRE  @0 35J10 @4 INC @5 74
C03 16  X  FRE  @0 47A10 @4 INC @5 75
C03 17  X  FRE  @0 62E17 @4 INC @5 76
C03 18  X  FRE  @0 Opérateur Laplace Beltrami @4 INC @5 77
C03 19  X  FRE  @0 Inégalité @4 CD @5 96
C03 19  X  ENG  @0 Inequality @4 CD @5 96
N21       @1 339
N44 01      @1 OTO
N82       @1 OTO

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Pascal:11-0490120

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