Rendiconti del Seminario Matematico della Università di Padova


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Volume 125, 2011, pp. 173–206
DOI: 10.4171/RSMUP/125-11

Conic Sheaves on Subanalytic Sites and Laplace Transform

Luca Prelli[1]

(1) Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Trieste, 63, 35121, Padova, Italy

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 $\mathcal O^{\mathrm{w}\land}_{E_{{\mathbb{R}^{{\scriptscriptstyle{+}}}}}}[n] \simeq \mathcal O^{\mathrm{w}}_{E^*_{{\mathbb{R}^{{\scriptscriptstyle{+}}}}}}$.

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Prelli Luca: Conic Sheaves on Subanalytic Sites and Laplace Transform. Rend. Sem. Mat. Univ. Padova 125 (2011), 173-206. doi: 10.4171/RSMUP/125-11