Conic Sheaves on Subanalytic Sites and Laplace Transform

Abstract

Let $E$ be a $n$ dimensional complex vector space and let $E^$ be its dual. We construct the conic sheaves $\mathcal O^t\_{E\_{{\mathbb{R}^{{\scriptscriptstyle{+}}}}}}$ and $\mathcal O^{\mathrm{w}}{E{{\mathbb{R}^{{\scriptscriptstyle{+}}}}}}$ of tempered and Whitney holomorphic functions respectively and we give a sheaf theoretical interpretation of the Laplace isomorphisms of \[10] which give the isomorphisms in the derived category $\mathcal O^{t\land}{E{{\mathbb{R}^{{\scriptscriptstyle{+}}}}}}\[n] \simeq \mathcal O^t\_{E^{{\mathbb{R}^{{\scriptscriptstyle{+}}}}}}$ and $\mathcal O^{\mathrm{w}\land}{E\_{{\mathbb{R}^{{\scriptscriptstyle{+}}}}}}\[n] \simeq \mathcal O^{\mathrm{w}}{E^\*{{\mathbb{R}^{{\scriptscriptstyle{+}}}}}}$.