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Localisation fréquentielle des paquets d'ondelettes.

Eric Séré — 1995

Revista Matemática Iberoamericana

Orthonormal bases of wavelet packets constitute a powerful tool in signal compression. It has been proved by Koifman, Meyer and Wickerhauser that many wavelet packets w suffer a lack of frequency localization. Using the L-norm of the Fourier transform ^w as localization criterion, they showed that the average 2Σ ||^w|| blows up as j goes to infinity. A natural problem is then to know which values of n create this blow-up in average. The present work gives an answer to this question,...

Les équations de Dirac-Fock

Maria J. EstebanEric Séré

Séminaire Équations aux dérivées partielles

Les équations de Dirac-Fock sont l’analogue relativiste des équations de Hartree-Fock. Elles sont utilisées dans les calculs numériques de la chimie quantique, et donnent des résultats sur les électrons dans les couches profondes des atomes lourds. Ces résultats sont en très bon accord avec les données expérimentales. Par une méthode variationnelle, nous montrons l’existence d’une infinité de solutions des équations de Dirac-Fock “sans projecteur", pour des systèmes coulombiens d’électrons dans...

General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators

Jean DolbeaultMaria EstebanEric Séré — 2006

Journal of the European Mathematical Society

This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.

Two Hartree-Fock models for the vacuum polarization

Philippe GravejatChristian HainzlMathieu LewinÉric Séré — 2012

Journées Équations aux dérivées partielles

We review recent results about the derivation and the analysis of two Hartree-Fock-type models for the polarization of vacuum. We pay particular attention to the variational construction of a self-consistent polarized vacuum, and to the physical agreement between our non-perturbative construction and the perturbative description provided by Quantum Electrodynamics.

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