Second microlocalization on involutive manifolds with regular projection property (Q914041)

This paper deals with the second analytic wave front set of distributions on involutive manifolds. The definition of this notion is given with the aid of a Fourier-Bros-Iagolnitzer phase function of the second kind. One shows that this definition does not depend on the choice of such a function. A result of microlocal regularity of the second kind for elliptic operators is obtained. Note that the theory presented here allows a complete study of hyperbolic operators with constant coefficients and of conical refraction in the case of operators with variable coefficients.