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{+}}}}}} .