A microlocal approach to the enhanced Fourier-Sato transform in dimension one

DOI10.1016/j.aim.2018.09.022zbMath1410.32007arXiv1709.03579OpenAlexW2756263607WikidataQ129202123 ScholiaQ129202123MaRDI QIDQ1989697

Masaki Kashiwara, Andrea D'Agnolo

Publication date: 29 October 2018

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.03579

zbMATH Keywords

Fourier transform\(\mathcal D\)-modulesmicrolocal study of sheavesstationary phase formulaenhanced ind-sheaves

Mathematics Subject Classification ID

Sheaves of differential operators and their modules, (D)-modules (32C38) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Asymptotic representations in the complex plane (30E15)

Related Items (6)

Formal stationary phase for the Mellin transform of a \(\mathcal{D}\)-module ⋮ Enhanced nearby and vanishing cycles in dimension one and Fourier transform ⋮ On Some Topological Properties of Fourier Transforms of Regular Holonomic -Modules ⋮ On a topological counterpart of regularization for holonomic \(\mathscr{D}\)-modules ⋮ On irregularities of Fourier transforms of regular holonomic \(\mathcal{D}\)-modules ⋮ D-modules of pure Gaussian type and enhanced ind-sheaves

Cites Work

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• Riemann-Hilbert correspondence for holonomic \(\mathcal{D}\)-modules
• Riemann-Hilbert correspondence for irregular holonomic \({\mathcal{D}}\)-modules
• The principle of stationary phase for the Fourier transform of D-modules
• Introduction to Stokes structures
• Calculation of \(\ell \)-adic local Fourier transformations
• The local Laplace transform of an elementary irregular meromorphic connection
• Irregular holonomic kernels and Laplace transform
• Note on the Stokes structure of Fourier transform
• The Riemann-Hilbert problem for holonomic systems
• Transformation de Fourier et majoration de sommes exponentielles. (Fourier transformation and majoration of exponential sums.)
• Fourier transformat, constants of the functional equations and Weil conjecture
• Differential equations with polynomial coefficients
• Calculation of local formal Fourier transforms
• Local Fourier transforms and rigidity for \({\mathcal D}\)-modules
• Microlocalization and stationary phase
• Differential systems of pure Gaussian type
• Regular and Irregular Holonomic D-Modules
• Local Fourier transform and epsilon factors
• Hasse-Arf filtrations in 𝑝-adic analytic geometry
• On the Laplace Transform for Tempered Holomorphic Functions
• An explicit stationary phase formula for the local formal Fourier-Laplace transform
• Rigid irregular connections on ℙ¹
• Product formula forp-adic epsilon factors
• Microlocal Theory of Sheaves and Tamarkin’s Non Displaceability Theorem

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