Existence of infinitely many homoclinic orbits in hamiltonian systems.
Looking for the Bernoulli shift
Localisation fréquentielle des paquets d'ondelettes.
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,...
Bases orthonormées de paquets d'ondelettes.
Les équations de Dirac-Fock
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
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.
A variational approach to homoclinic orbits in Hamiltonian systems.
Two Hartree-Fock models for the vacuum polarization
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.
About a non-homogeneous Hardy-inequality and its relation with the spectrum of Dirac operators
A non-homogeneous Hardy-like inequality has recently been found to be closely related to the knowledge of the lowest eigenvalue of a large class of Dirac operators in the gap of their continuous spectrum.
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