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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 transform
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by Masaki Kashiwara and Pierre Schapira PDF
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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Additional Information
  • Masaki Kashiwara
  • Affiliation: RIMS, Kyoto University, Kyoto 606-01, Japan
  • MR Author ID: 98845
  • Pierre Schapira
  • Affiliation: Institut de Mathématiques, Université Paris VI, Case 82, 4 pl Jussieu, 75252 Paris, France
  • Email: schapira@math.jussieu.fr
  • Received by editor(s): September 17, 1996
  • Received by editor(s) in revised form: May 23, 1997
  • © Copyright 1997 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 10 (1997), 939-972
  • MSC (1991): Primary 32C38, 14F10, 44A10
  • DOI: https://doi.org/10.1090/S0894-0347-97-00245-2
  • MathSciNet review: 1447834