Jean Nourrigat

La condition de hörmander-khon pour les operateurs pseudo-differentiels

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On bounded pseudodifferential operators in a high-dimensional setting

This work is concerned with extending the results of Calderon and Vaillancourt proving the boundedness of Weyl pseudodifferential operators Op W eyl h (F) in L 2 (R n). We state conditions under which the norm of such operators has an upper bound independent of n. To this aim, we apply a decomposition of the identity to the symbol F , thus obtaining a sum of operators of a hybrid type, each of them behaving as a Weyl operator with respect to some of the variables and as an anti-Wick operator with respect to the other ones. Then we establish upper bounds for these auxiliary operators, using suitably adapted classical methods like coherent states.

The semiclassical limit of the time dependent Hartree–Fock equation: The Weyl symbol of the solution

We study the Wick symbol of a solution of the time dependent Hartree Fock equation, under weaker hypotheses than those needed for the Weyl symbol in the first paper with thesame title. With similar, we prove some kind of Ehrenfest theorem for observables that are not pseudo-differential operators.

Weyl calculus in QED I. The unitary group

In this work, we consider fixed

Resonances of the Dirac Hamiltonian in the Non Relativistic Limit

1/2

Thermodynamic Limits for Hamiltonians Defined as Pseudodifferential Operators

spin particles interacting with the quantized radiation field in the context of quantum electrodynamics (QED). We investigate the time evolution operator in studying the reduced propagator (interaction picture). We first prove that this propagator belongs to the class of infinite dimensional Weyl pseudodifferential operators recently introduced in \cite {A-J-N} on Wiener spaces. We give a semiclassical expansion of the symbol of the reduced propagator up to any order with estimates on the remainder terms. Next, taking into account analyticity properties for the Weyl symbol of the reduced propagator, we derive estimates concerning transition probabilities between coherent states.

Borne inférieure du spectre de l'opérateur de Schrödinger@@@Lower bound for the spectrum of the Schrödinger operator

Abstract. For a Dirac operator in

Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs

{\Bbb R}^3

A necessary and sufficient condition for Melin’s inequality for a class of systems

, with an electric potential behaving at infinity like a power of |x|, we prove the existence of resonances and we study, when

Dynamics and Lieb-Robinson estimates for lattices of interacting anharmonic oscillators

c \rightarrow + \infty