Semi classical analysis for perturbation of periodic operators
Identifieur interne : 000008 ( France/Analysis ); précédent : 000007; suivant : 000009Semi classical analysis for perturbation of periodic operators
Auteurs : Youssef Sbai [France]Source :
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Abstract
This Ph.D thesis deals with some spectral properties of two specific classes of two periodic operators. We are firstly interested in the model periodic perturbed by operator depending on a small semi-classical constant. We obtain an asymptotic behavior of the eigenvalue counting function in the spectral gaps with scharp remainder estimate. The second model studied in this thesis is a two-dimensional periodic elliptic second order opera-tor perturbed by operator depending on a large coupling constant. We also give the description of the counting function of eigenvalues when the coupling constant tends to infinity. The last part of this thesis highlights the study the spectrum of a Schrödinger operator perturbed by a fast oscillatingdecaying potential depending on a small parameter.
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We are firstly interested in the model periodic perturbed by operator depending on a small semi-classical constant. We obtain an asymptotic behavior of the eigenvalue counting function in the spectral gaps with scharp remainder estimate. The second model studied in this thesis is a two-dimensional periodic elliptic second order opera-tor perturbed by operator depending on a large coupling constant. We also give the description of the counting function of eigenvalues when the coupling constant tends to infinity. The last part of this thesis highlights the study the spectrum of a Schrödinger operator perturbed by a fast oscillatingdecaying potential depending on a small parameter.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Aquitaine</li></region><settlement><li>Bordeaux</li></settlement><orgName><li>Université de Bordeaux</li></orgName></list><tree><country name="France"><region name="Aquitaine"><name sortKey="Sbai, Youssef" sort="Sbai, Youssef" uniqKey="Sbai Y" first="Youssef" last="Sbai">Youssef Sbai</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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