Relative subanalytic sheaves

Abstract

Given a projection $f$ of a product of real analytic manifolds onto one factor, let us say, $S$, and a subanalytic sheaf $\mathcal{F}$ on the associated subanalytic site, we give a natural construction of the (subanalytic) relative sheaf ${\mathcal{F}}^S$. Applying our construction to the subanalytic sheaves of tempered distributions, holomorphic functions and Whitney ${\mathcal{C}}^{\infty }$-functions we obtain their relative versions and study their properties.

18 pages