解析学火曜セミナー

過去の記録 ~07/20次回の予定今後の予定 07/21~

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/

2023年06月06日(火)

17:00-18:30   数理科学研究科棟(駒場) 128号室
対面・オンラインハイブリッド開催,通常とは時間と場所が異なります
Erik Skibsted 氏 (Aarhus University)
Stationary completeness; the many-body short-range case (English)
[ 講演概要 ]
For a general class of many-body Schr\"odinger operators with short-range pair-potentials the wave and scattering matrices as well as the restricted wave operators are all defined at any non-threshold energy. In fact this holds without imposing any a priori decay condition on channel eigenstates and even for models including long-range potentials of Derezi\'nski-Enss type. For short-range models we improve on the known \emph{weak continuity} statements in that we show that all non-threshold energies are \emph{stationary complete}, resolving in this case a recent conjecture. A consequence is that the above scattering quantities depend \emph{strongly continuously} on the energy parameter at all non-threshold energies (whence not only almost everywhere as previously demonstrated). Another consequence is that the scattering matrix is unitary at any such energy. Our procedure yields (as a side result) a new and purely stationary proof of asymptotic completeness for many-body short-range systems.
[ 参考URL ]
https://forms.gle/kWHDfb6J6kcjfSah8