Micro-support and Cauchy problem for temperate solutions of regular $\mathcal{D}$-Modules

Abstract

Let $X$ be a complex manifold, $V$ a smooth involutive submanifold of $T^{\ast }X$, $\mathcal{M}$ a microdifferential system regular along $V$, and $F$ an $\mathbb{R}$-constructible sheaf on $X$. The complex of temperate microfunction solutions of $\mathcal{M}$ associated with $F$ is now well understood. In this paper we study the temperate case and give a bound to the micro-support of the temperate microfunction solution sheaves and solve the Cauchy problem under suitable hyperbolicity conditions.

20 pages, Latex 2e, correct some typos on the abstract, which incorrectly used macros