Maher Zerzeri

A local trace formula for resonances of perturbed periodic Schrödinger operators

Abstract We give a local trace formula for the pair ( P 1 ( h )= P 0 + W ( hy ), P 0 ), where P 0 is a periodic Schrodinger operator, W is a decreasing perturbation and h is a small positive parameter. We apply this result to establish the existence of ∼ h − n resonances near some energy λ of σ ( P 0 ).

Spectral shift function for perturbed periodic Schrödinger operators. The large-coupling constant limit case

In the large coupling constant limit, we obtain an asymptotic expansion in powers of

Microlocal kernel of pseudodifferential operators at a hyperbolic fixed point

\mu^{-\frac{1}{\delta}}

Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances

of the derivative of the spectral shift function corresponding to the pair

Resonances for homoclinic trapped sets

\big(P_\mu=P_0+\mu W(x),P_0=-\Delta+V(x)\big),

The rate at which energy decays in a viscously damped hinged Euler–Bernoulli beam

where

MAJORATION DU NOMBRE DE RÉSONANCES PRÈS DE L'AXE RÉEL POUR UNE PERTURBATION ABSTRAITE À SUPPORT COMPACT DU LAPLACIEN

W(x)

On the classical limit of self-interacting quantum field Hamiltonians with cutoffs

is positive,

Barrier-top resonances for non globally analytic potentials

W(x)\sim w_0(\frac{x}{|x|})|x|^{-\delta}

Propagation des singularit\'es et r\'esonances

near infinity for some