Jecko Th.
Semiclassical resolvent estimates for Schr\"odinger matrix 
operators with eigenvalues crossing.
(109K, LaTeX 2e)

ABSTRACT.  For semiclassical Schr\"odinger matrix operators, we investigate the 
semiclassical Mourre theory to derive semiclassical bounds for the 
boundary values of the resolvent. We concentrate on the case where 
the eigenvalues of the symbol cross. Under the non-trapping condition 
on the eigenvalues of the symbol and under a condition on its matricial 
structure, we obtain the desired bounds for codimension one crossings. 
For codimension two crossings, we show that a geometrical condition 
at the crossing must hold to get the existence of a global escape 
function, required by the usual semiclassical Mourre theory.