Specialization of Formal Cohomology and Asymptotic Expansions

Abstract

Following a work of Andronikof, we build a theory of Whitney specialization for $C^{\infty }$-functions and holomorphic functions. To an $R$-constructible sheaf, we associate a $\mathcal{D}$-module. In particular, the constant sheaf gives the germs of functions asymptotically developable.