# Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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## Integral transforms with exponential kernels and Laplace transformHTML articles powered by AMS MathViewer

by Masaki Kashiwara and Pierre Schapira
J. Amer. Math. Soc. 10 (1997), 939-972 Request permission

## Abstract:

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*} &F \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.
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