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解析学火曜セミナー
過去の記録 ～10/04｜次回の予定｜今後の予定 10/05～
| 開催情報 | 火曜日 16:00～17:30 数理科学研究科棟(駒場) 156号室 |
|---|---|
| 担当者 | 石毛 和弘, 坂井 秀隆, 伊藤 健一 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/analysis/ |
2015年04月21日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
今年度から部屋が１２６に変わりました．
松原 宰栄 氏 (東京大学大学院数理科学研究科)
留数カレントと定数係数線形遅延微分方程式系の一般論について (Japanese)
今年度から部屋が１２６に変わりました．
松原 宰栄 氏 (東京大学大学院数理科学研究科)
留数カレントと定数係数線形遅延微分方程式系の一般論について (Japanese)
[ 講演概要 ]
We introduce the ring of differential operators with constant coefficients and commensurate time lags (we use the terminology D$\Delta$ operators from now) initially defined by H. Gl\"using-L\"ur\ss en for ordinary $D\Delta$ operators and observe that various function modules enjoy good cohomological properties over this ring. %After revising the notion of the residue current in the spirit of M. Andersson and E. Wulcan, we introduce the multidimensional version of the ring D$\Delta$ operators.
Combining this ring theoretic observation with the integral representation technique developed by M. Andersson, we solve a certain type of division with bounds. In the last chapter, we prove the injectivity property of various function modules over this ring as well as spectral synthesis type theorems for $D\Delta$ equations.
We introduce the ring of differential operators with constant coefficients and commensurate time lags (we use the terminology D$\Delta$ operators from now) initially defined by H. Gl\"using-L\"ur\ss en for ordinary $D\Delta$ operators and observe that various function modules enjoy good cohomological properties over this ring. %After revising the notion of the residue current in the spirit of M. Andersson and E. Wulcan, we introduce the multidimensional version of the ring D$\Delta$ operators.
Combining this ring theoretic observation with the integral representation technique developed by M. Andersson, we solve a certain type of division with bounds. In the last chapter, we prove the injectivity property of various function modules over this ring as well as spectral synthesis type theorems for $D\Delta$ equations.
