2013 Fiscal Year Final Research Report
Microlocal analysis of topological Radon transforms and their application to singularity thoery
| Project/Area Number |
23740134
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Kinki University |
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Principal Investigator |
MATSUI Yutaka 近畿大学, 理工学部, 准教授 (10510026)
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| Project Period (FY) |
2011 – 2013
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| Keywords | ラドン変換 / グラスマン多様体 / 構成可能関数 / 超局所解析 |
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| Research Abstract |
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.
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Research Products
(13 results)
