Two-microlocal semi-classical measures

Let (u(h)) be a uniformly bounded family in L-2(R-d) and I an involutive submanifold of T*R-d. In this Note, we introduce two items which describe the concentration of(uh) on I. The first one is a 2-microlocal item: a positive Radon measure on the homogeneous normal bundle to I. The second one is a trace-class operator-valued measure. The knowledge of these two items determines above I the semi-classical measure of the family (u(h)). (C) 2000 Academie des sciences Editions scientifiques et medicales Elsevier SAS.