東京大学大学院数理科学研究科
Graduate School of Mathematical Sciences, The University of Tokyo
Abstract
The present thesis consists of the two part:/ I Generalized Okubo systems and the middle convolution / II Confluence of singular points and the Okubo systems In the first part, we give a generalization, called a generalized Okubo system, of a system of linear differential equations of the Okubo normal form and define a mapping π from a set of generalized Okubo systems to a set of linear differential systems. We consider the operation, the middle convolution introduced by Katz, using π, and show that any system of linear differential equations, not necessarily of the Fuchsian type, with a regular singularity at infinity, can be transformed into generalized Okubo system. For any non-Fuchsian system, we can construct a Fuchsian system with a parameter ε which tends to the given equation as ε→ 0. In the second part, we consider a confluence of the convolution in the sense of Katz-Dettweiler-Reiter and we show that convolutions of each equation is compatiple with the confluence.
発行年
2009-03-23
日本十進分類法
410
学位名
博士(数理科学)
学位
doctoral
学位分野
Mathematical Sciences (数理科学)
学位授与機関
University of Tokyo (東京大学)
研究科・専攻
Graduate School of Mathematical Sciences (数理科学研究科)
学位授与年月日
2009-03-23
学位授与番号
甲第24974号
学位記番号
博数理第329号
アイテムへのリンクの際はタイトル右肩にある「Permalink」をご利用ください！
Please use "Permalink" at the top right of the title when linking to items!
Generalized Okubo systems and the middle convolution
HiroshiK_21_3_PhD_a.pdf
(3.09MB)
