Measures on double or resonant eigenvalues for linear Schrödinger operator

Didier Bresch; Benoît Desjardins; Emmanuel Grenier

doi:10.1016/j.jfa.2007.11.009

Measures on double or resonant eigenvalues for linear Schrödinger operator

Didier Bresch^*
, Benoît Desjardins
, Emmanuel Grenier

^*Corresponding author for this work

Université Savoie Mont Blanc
Modélisation Mesures et Applications S.A.
École normale supérieure
Unité de Mathématiques Pures et Appliquées de l'ENS de Lyon

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we consider linear Schrödinger operator with double or resonant eigenvalues. The main result is the bound of the measure (in a suitable space of functions) of the potentials leading to such double or resonant eigenvalues. Namely we present measure type estimates evaluating neighborhoods of the so-called double or resonant set.

Original language	English
Pages (from-to)	1269-1281
Number of pages	13
Journal	Journal of Functional Analysis
Volume	254
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2007.11.009
Publication status	Published - 1 Mar 2008
Externally published	Yes

Keywords

Linear Schrödinger operator
Measure type estimates
Multiple eigenvalues
Resonant set

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10.1016/j.jfa.2007.11.009

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title = "Measures on double or resonant eigenvalues for linear Schr{\"o}dinger operator",

abstract = "In this paper we consider linear Schr{\"o}dinger operator with double or resonant eigenvalues. The main result is the bound of the measure (in a suitable space of functions) of the potentials leading to such double or resonant eigenvalues. Namely we present measure type estimates evaluating neighborhoods of the so-called double or resonant set.",

keywords = "Linear Schr{\"o}dinger operator, Measure type estimates, Multiple eigenvalues, Resonant set",

author = "Didier Bresch and Beno{\^i}t Desjardins and Emmanuel Grenier",

year = "2008",

month = mar,

day = "1",

doi = "10.1016/j.jfa.2007.11.009",

language = "English",

volume = "254",

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journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Measures on double or resonant eigenvalues for linear Schrödinger operator

AU - Bresch, Didier

AU - Desjardins, Benoît

AU - Grenier, Emmanuel

PY - 2008/3/1

Y1 - 2008/3/1

N2 - In this paper we consider linear Schrödinger operator with double or resonant eigenvalues. The main result is the bound of the measure (in a suitable space of functions) of the potentials leading to such double or resonant eigenvalues. Namely we present measure type estimates evaluating neighborhoods of the so-called double or resonant set.

AB - In this paper we consider linear Schrödinger operator with double or resonant eigenvalues. The main result is the bound of the measure (in a suitable space of functions) of the potentials leading to such double or resonant eigenvalues. Namely we present measure type estimates evaluating neighborhoods of the so-called double or resonant set.

KW - Linear Schrödinger operator

KW - Measure type estimates

KW - Multiple eigenvalues

KW - Resonant set

UR - https://www.scopus.com/pages/publications/38649141173

U2 - 10.1016/j.jfa.2007.11.009

DO - 10.1016/j.jfa.2007.11.009

M3 - Article

AN - SCOPUS:38649141173

SN - 0022-1236

VL - 254

SP - 1269

EP - 1281

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 5

ER -

Measures on double or resonant eigenvalues for linear Schrödinger operator

Abstract

Keywords

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