H2N2V1, PascalFrancis, Checkpoint, bibRecord, 000009

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

Identifieur interne : 000009 ( PascalFrancis/Checkpoint ); précédent : 000008; suivant : 000010

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

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

Source :

Transactions of the American Mathematical Society [ 0002-9947 ] ; 2011.

RBID : Pascal:11-0490120

Descripteurs français

Pascal (Inist)
- Trace, Distribution, Fonction répartition, Valeur propre, Règle somme, Opérateur Schrödinger, Variété mathématique, Borne inférieure, Monotonie, Moment statistique, 60E05, 65F15, 65H17, Opérateur périodique, 35J10, 47A10, 62E17, Opérateur Laplace Beltrami, Inégalité.

English descriptors

KwdEn :
- Distribution, Distribution function, Eigenvalue, Inequality, Lower bound, Manifold, Monotonicity, Schrödinger operator, Statistical moment, Sum rule, Trace.

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 λ_N+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 λ_N+1 of the Laplace-Beltrami operator by a universal constant times ⁄h⁄²∞N^2/d.

Affiliations:

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Le document en format XML

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<front><div type="abstract" xml:lang="en">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 λ<sub>N+1</sub>
 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 λ<sub>N+1</sub>
 of the Laplace-Beltrami operator by a universal constant times ⁄h⁄<sup>2</sup>
∞N<sup>2/d</sup>
.</div>
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 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 λ<sub>N+1</sub>
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<fC03 i1="01" i2="X" l="SPA"><s0>Traza</s0>
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<fC03 i1="02" i2="X" l="ENG"><s0>Distribution</s0>
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<s5>20</s5>
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<fC03 i1="04" i2="X" l="SPA"><s0>Valor propio</s0>
<s5>20</s5>
</fC03>
<fC03 i1="05" i2="X" l="FRE"><s0>Règle somme</s0>
<s5>21</s5>
</fC03>
<fC03 i1="05" i2="X" l="ENG"><s0>Sum rule</s0>
<s5>21</s5>
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<fC03 i1="05" i2="X" l="SPA"><s0>Regla suma</s0>
<s5>21</s5>
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<s5>22</s5>
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<s5>23</s5>
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<s5>23</s5>
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<s5>24</s5>
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<s5>24</s5>
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<s5>26</s5>
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<s5>26</s5>
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<s5>26</s5>
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<fC03 i1="11" i2="X" l="FRE"><s0>60E05</s0>
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<s5>70</s5>
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<s4>INC</s4>
<s5>71</s5>
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<fC03 i1="13" i2="X" l="FRE"><s0>65H17</s0>
<s4>INC</s4>
<s5>72</s5>
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<fC03 i1="14" i2="X" l="FRE"><s0>Opérateur périodique</s0>
<s4>INC</s4>
<s5>73</s5>
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<s4>INC</s4>
<s5>74</s5>
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<s4>INC</s4>
<s5>75</s5>
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<fC03 i1="17" i2="X" l="FRE"><s0>62E17</s0>
<s4>INC</s4>
<s5>76</s5>
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<fC03 i1="18" i2="X" l="FRE"><s0>Opérateur Laplace Beltrami</s0>
<s4>INC</s4>
<s5>77</s5>
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<fC03 i1="19" i2="X" l="FRE"><s0>Inégalité</s0>
<s4>CD</s4>
<s5>96</s5>
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<s4>CD</s4>
<s5>96</s5>
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<fN21><s1>339</s1>
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TRACE IDENTITIES FOR COMMUTATORS, WITH APPLICATIONS TO THE DISTRIBUTION OF EIGENVALUES

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

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

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