Microlocal analysis of topological Radon transforms and their application to singularity thoery

拓扑Radon变换的微局域分析及其在奇点理论中的应用

• 批准号: 23740134
• 负责人: MATSUI Yutaka
• 金额: $ 1.5万
• 依托单位: Kinki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740134/
• 关键词: ラドン変換; グラスマン多様体; 構成可能関数; 超局所解析; 国際情報交流; 国際情報交換

In this research, we study integral transforms of constructible functions, whose integral theory is based on the Euler characteristic. We proved that the images of topological Radon transforms on Grassmann manifolds satisfy a system of topological integral equations. Note that in the analytic case the images satisfy a system of partial differential equations.We also prove an inversion formula for topological Radon transforms of definable functions, which are more general than constructible functions.

本文研究了可构造函数的积分变换，其积分理论是基于欧拉特征线的。证明了Grassmann流形上拓扑Radon变换的象满足一个拓扑积分方程组。注意在解析情形下图像满足一个偏微分方程组，我们还证明了可定义函数的拓扑Radon变换的反演公式，这比可构造函数更一般。

项目成果

Topological Radon transforms on Grassmann manifolds

格拉斯曼流形上的拓扑氡变换

• 作者: M. Shimojo and T;Kagaya;青井久;青井久;青井久;Masahiko Shimojo;下條 昌彦;Yusuke Yamauchi;Masahiko Shimojo;下條 昌彦;N. Hayashi and Y. Matsui;Naoya HAYASHI and Yutaka MATSUI;Y. Yamauchi;竹内 潔,松井 優;Y. Yamauchi;Y. Matsui and K. Takeuchi;Y. Matsui and K. Takeuchi;Y. Yamauchi;Yutaka MATSUI;Life span of positive solutions for a semilinear heat equation with nondecaying initial data;Y. Matsui;Y. Matsui;Yutaka MATSUI;Yutaka MATSUI
• 通讯作者: Yutaka MATSUI

Topological Radon transforms and their applications

拓扑Radon变换及其应用

• 发表时间: 2008
• 期刊: RIMS kokyuroku bessatsu B5
• 作者: 竹内潔;松井優
• 通讯作者: 松井優

多項式写像とA-超幾何関数の無限遠点におけるモノドロミー

多项式映射和A-超几何函数的无穷远单向性

• 发表时间: 2012
• 期刊: 数学
• 作者: M. Shimojo and T;Kagaya;青井久;青井久;青井久;Masahiko Shimojo;下條 昌彦;Yusuke Yamauchi;Masahiko Shimojo;下條 昌彦;N. Hayashi and Y. Matsui;Naoya HAYASHI and Yutaka MATSUI;Y. Yamauchi;竹内 潔,松井 優
• 通讯作者: 竹内 潔,松井 優

Decomposition formulae for generalized hypergeometric functions with the Gauss-Kummer identity

具有 Gauss-Kummer 恒等式的广义超几何函数的分解公式

• 发表时间: 2014
• 期刊: Commun. Korean Math
• 作者: M. Shimojo and T;Kagaya;青井久;青井久;青井久;Masahiko Shimojo;下條 昌彦;Yusuke Yamauchi;Masahiko Shimojo;下條 昌彦;N. Hayashi and Y. Matsui
• 通讯作者: N. Hayashi and Y. Matsui

Topological Radon transforms with modified kernels on Grassmann manifolds

使用修改后的核在格拉斯曼流形上进行拓扑氡变换

• 发表时间: 2011
• 期刊: RIMS講究録
• 作者: M. Shimojo and T;Kagaya;青井久;青井久;青井久;Masahiko Shimojo;下條 昌彦;Yusuke Yamauchi;Masahiko Shimojo;下條 昌彦;N. Hayashi and Y. Matsui;Naoya HAYASHI and Yutaka MATSUI;Y. Yamauchi;竹内 潔,松井 優;Y. Yamauchi;Y. Matsui and K. Takeuchi;Y. Matsui and K. Takeuchi;Y. Yamauchi;Yutaka MATSUI
• 通讯作者: Yutaka MATSUI