Integral Transforms with Exponential Kernels and Laplace Transform
نویسندگان
چکیده
Let X ←−fZ −→gY be a correspondence of complex manifolds. We study integral transforms associated to kernels exp(φ), with φ meromor-phic on Z, acting on formal or moderate cohomologies. Our main applicationis the Laplace transform. In this case, X is the projective compactification ofthe vector space V ' Cn, Y is its dual space, Z = X×Y and φ(z, w) = 〈z,w〉.We obtain the isomorphisms: F W⊗ OV ' F∧[n] W⊗ OV ∗ ,THom(F,OV ) 'THom(F∧[n],OV ∗ ) License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use 972MASAKI KASHIWARA AND PIERRE SCHAPIRA where F is a conic and R-constructible sheaf on V and F∧ is its Fourier-Satotransform. Some applications are discussed. RIMS, Kyoto University, Kyoto 606-01, Japan Institut de Mathématiques, Université Paris VI, Case 82, 4 pl Jussieu, 75252 Paris,FranceE-mail address: [email protected] License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use
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