Carleman regularization in the \(C^\infty\)-category (Q2756127)

The purpose of this methodical article is to describe a number of classical facts in the theory of \(C^{\infty}\)-microlocalization with arguments naturally associated with microlocal analysis in the analytic category. In this category microlocal arguments can be based on two rather different points of view. One was initiated by M. Sato and relies on sheaf-theoretic and cohomological methods. The other point of view was introduced by Hörmander and relies mainly on the theory of the Fourier-transform. The author shows how this transform relates analytic notions to the corresponding geometric objects.