Second analytic wave front set of the fundamental solutions of hyperbolic operators

Abstract

The notion of a second microlocalization along an involutive submanifold WCIS introduced by M. Kashiwara [6] .Y. Laurent developed this notion and established a theory of the 2-microdifferential operators [8]. In [Ill, 3 . Sjostrand defined the second analytic wave front set (and even a kth wave front set) along the lagrangian submanifolds.So he was able to get a result of M. Kashiwara and to generalize it. This result provides very strict relations between the support and the wave front set, and, as a generalization, between the (k-l)th wave front set and the kth one. J.M.Bony gave a definition adapted to the frame of the C∞o-singularities. Finally G. Lebeau spread the notion to the isotropic manifolds and applied it to a degenerated diffraction problem.