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Irregular holonomic kernels and Laplace transform. (English) Zbl 1337.32020
Authors’ abstract: Given a (not necessarily regular) holonomic \(\mathcal D\)-module \(\mathcal L\) defined on the product of two complex manifolds, we prove that the correspondence associated with \(\mathcal L\) commutes (in some sense) with the de Rham functor. We apply this result to the study of the classical Laplace transform. The main tools used here are the theory of ind-sheaves and its enhanced version.

MSC:
32C38 Sheaves of differential operators and their modules, \(D\)-modules
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
44A10 Laplace transform
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