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Onétudie des estimations semiclassiques sur la résolvente d'opérateurs qui ne sont ni ellip-tiques ni autoadjoints, que l'on utilise pourétudier leprobì eme de Cauchy. En particulier on obtient une description précise du spectre pres de l'axe imaginaire, et des estimations de résolventè a l'intérieur du pseudo-spectre. On applique ensuite les résultatsà(More)
In this paper we show, in dimension n ≥ 3, that knowledge of the Cauchy data for the Schrödinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential. We follow the general strategy of [7] using a richer set of solutions to the Dirichlet(More)
Considèrons un opérateur h-pseudodifférentiel, dont le symbole p s'´ etend holomorphiquement` a un voisinage tubulaire de l'espace de phase réel et converge assez vite vers 1, pour que le déterminant soit bien défini. Nous montrons que le logarithme du module du déterminant est majoré par (2πh) −n (I(Λ, p) + o(1)), h → 0, o` u I(Λ, p) est l'intégrale de log(More)
We consider quite general h-pseudodifferential operators on R n with small random perturbations and show that in the limit h → 0 the eigenvalues are distributed according to a Weyl law with a probabality that tends to 1. The first author has previously obtained a similar result in dimension 1. Our class of perturbations is different. Résumé Nous considérons(More)
We consider operators of Kramers-Fokker-Planck type in the semi-classical limit such that the exponent of the associated Maxwellian is a Morse function with two local minima and a saddle point. Under suitable additional assumptions we establish the complete asymptotics of the exponentially small splitting between the first two eigenvalues. Résumé On(More)
Trace formulae provide one of the most elegant descriptions of the classical-quantum correspondence. One side of a formula is given by a trace of a quantum object, typically derived from a quantum Hamiltonian, and the other side is described in terms of closed orbits of the corresponding classical Hamiltonian. In algebraic situations, such as the original(More)