Resolvent estimates and matrix-valued Schrodinger operator with eigenvalue crossings; Application to Strichartz estimates
Résumé
We consider a semi-classical Schrodinger operator with a matrix-valued potential presenting eigenvalue crossings on isolated points. We obtain estimates for the boundary values of the resolvent under a generalized non-trapping assumption. As a consequence, we prove the smoothing effect of this operator, derive Strichartz type estimate for the propagator and get an existence theorem for a system of non-linear Schrodinger equations.