Geodesic
Integral transforms with exponential kernels and Laplace transform
Kashiwara, Masaki1 ; Schapira, Pierre2
1 RIMS, Kyoto University, Kyoto 606-01, Japan
2 Institut de Mathématiques, Université Paris VI, Case 82, 4 pl Jussieu, 75252 Paris, France
Journal of the American Mathematical Society, Tome 10 (1997) no. 4, pp. 939-972

Voir la notice de l'article provenant de la source American Mathematical Society

Let $X \underset {f}{\longleftarrow } Z \underset {g}{\longrightarrow } Y$ be a correspondence of complex manifolds. We study integral transforms associated to kernels $\exp (\varphi )$, with $\varphi$ meromorphic on $Z$, acting on formal or moderate cohomologies. Our main application is the Laplace transform. In this case, $X$ is the projective compactification of the vector space $V \simeq \mathbb {C}^n$, $Y$ is its dual space, $Z=X\times Y$ and $\varphi (z,w) =\langle z,w \rangle$. We obtain the isomorphisms: \begin{align*} \otimes ^W \mathcal {O}_V \simeq F^\wedge [n] \otimes ^W \mathcal {O}_{V^*},\quad \operatorname {THom}(F,\mathcal {O}_V) \simeq \operatorname {THom}(F^\wedge [n],\mathcal {O}_{V^*}) \end{align*} where $F$ is a conic and $\mathbb {R}$-constructible sheaf on $V$ and $F^\wedge$ is its Fourier-Sato transform. Some applications are discussed.
DOI : 10.1090/S0894-0347-97-00245-2

Kashiwara, Masaki 1 ; Schapira, Pierre 2

1 RIMS, Kyoto University, Kyoto 606-01, Japan
2 Institut de Mathématiques, Université Paris VI, Case 82, 4 pl Jussieu, 75252 Paris, France 
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Kashiwara, Masaki; Schapira, Pierre. Integral transforms with exponential kernels and Laplace transform. Journal of the American Mathematical Society, Tome 10 (1997) no. 4, pp. 939-972. doi: 10.1090/S0894-0347-97-00245-2

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