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Lie群論・表現論セミナー
過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 開催情報 | 火曜日 16:30～18:00 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 小林俊行 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html |
2006年07月25日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Boris Rubin 氏 (Louisiana State University)
Radon Transforms: Basic Concepts
http://akagi.ms.u-tokyo.ac.jp/seminar.html
Boris Rubin 氏 (Louisiana State University)
Radon Transforms: Basic Concepts
[ 講演概要 ]
How can we reconstruct a function on a manifold from integrals of this function over certain submanifolds?
This is one of the central problems in integral geometry and tomography, which leads to the notion of the Radon transform.
The first talk is of introductory character.
We discuss basic ideas of the original Radon's paper (1917), then proceed to the Minkowski-Funk transform and more general totally geodesic Radon transforms on the $n$-dimensional unit sphere.
The main emphasis is an intimate connection of these transforms with the relevant harmonic analysis.
We will see that Radon transforms of this type and their inverses can be regarded as members of analytic families of suitable convolution operators and successfully studied in the framework of these families.
I also plan to discuss an open problem of small divisors on the unit sphere, which arises in studying injectivity of generalized Minkowski-Funk transforms for non-central spherical sections.
[ 参考URL ]How can we reconstruct a function on a manifold from integrals of this function over certain submanifolds?
This is one of the central problems in integral geometry and tomography, which leads to the notion of the Radon transform.
The first talk is of introductory character.
We discuss basic ideas of the original Radon's paper (1917), then proceed to the Minkowski-Funk transform and more general totally geodesic Radon transforms on the $n$-dimensional unit sphere.
The main emphasis is an intimate connection of these transforms with the relevant harmonic analysis.
We will see that Radon transforms of this type and their inverses can be regarded as members of analytic families of suitable convolution operators and successfully studied in the framework of these families.
I also plan to discuss an open problem of small divisors on the unit sphere, which arises in studying injectivity of generalized Minkowski-Funk transforms for non-central spherical sections.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
