A microlocal approach to the enhanced Fourier-Sato transform in dimension one
A microlocal approach to the enhanced Fourier-Sato transform in dimension one
复制标题
一维增强傅里叶-佐藤变换的微局域方法
DOI：
10.1016/j.aim.2018.09.022
复制
发表时间：
2018
影响因子：
1.7
通讯作者：
Kashiwara Masaki
中科院分区：
文献类型：
--
作者：
D'Agnolo Andrea;Kashiwara Masaki
设M是仿射线上的完整代数D-模。它的指数因子是描述M的全纯解在不规则点处增长的Puiphix芽。固定相公式指出，M的傅里叶变换的指数因子由M的指数因子通过勒让德变换获得。我们给出了一个微局部证明这一事实，通过翻译它的增强ind-sheaves通过黎曼-希尔伯特对应。
Let M be a holonomic algebraic D-module on the affine line. Its exponential factors are Puiseux germs describing the growth of holomorphic solutions to M at irregular points. The stationary phase formula states that the exponential factors of the Fourier transform of M are obtained by Legendre transform from the exponential factors of M. We give a microlocal proof of this fact, by translating it in terms of enhanced ind-sheaves through the Riemann–Hilbert correspondence.