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On irregularities of Fourier transforms of regular holonomic \(\mathcal{D}\)-modules. (English) Zbl 07183749
Summary: We study Fourier transforms of regular holonomic \(\mathcal{D}\)-modules. By using the theory of Fourier-Sato transforms of enhanced ind-sheaves developed by Kashiwara-Schapira and D’Agnolo-Kashiwara, a formula for their enhanced solution complexes will be obtained. Moreover we show that some parts of their characteristic cycles and irregularities are expressed by the geometries of the original \(\mathcal{D}\)-modules.

MSC:
32C38 Sheaves of differential operators and their modules, \(D\)-modules
32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
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