Conic Sheaves on Subanalytic Sites and Laplace Transform

  • Luca Prelli

    Università di Padova, Italy


Let EE be a nn dimensional complex vector space and let EE^* be its dual. We construct the conic sheaves OER+t\mathcal O^t_{E_{{\mathbb{R}^{{\scriptscriptstyle{+}}}}}} and OER+w\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{+}}}}}}.

Cite this article

Luca Prelli, Conic Sheaves on Subanalytic Sites and Laplace Transform. Rend. Sem. Mat. Univ. Padova 125 (2011), pp. 173–206

DOI 10.4171/RSMUP/125-11