Construction of abstract theory for Schrodinger evolution equations

• Project/Area Number: 15K17558
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Kanagawa University (2017); Tokyo University of Science (2015-2016)
• Principal Investigator: Yoshii Kentarou 神奈川大学, 工学部, 非常勤講師 (00632449)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 抽象発展方程式 / シュレディンガー発展方程式 / 双曲型制御問題 / リパルシブ・ハミルトニアン / 双曲型発展方程式 / 時間依存型ユニタリー変換 / 摂動論 / 一般コーシー問題

Outline of Final Research Achievements

We could not construct abstract theory for Schrodinger evolution equations.
However, we obtained small results.
One is the solvability of a kind of optimal control problem for Schrodinger evolution equations. Next one is the partial expansion of the scattering theorem for Repulsive Hamiltonian. These studies are important foundations in applied analysis.

Research Products

• [Presentation] An Embedding Estimate for the Repulsive Hamiltonian (2016)
  • Author(s): 吉井健太郎
  • Organizer: 11th AIMS International Conference on DSDEA
  • Place of Presentation: Orlando(アメリカ)
  • Int'l Joint Research
• [Presentation] An Embedding Estimate for the Repulsive Hamiltonian in Lp (2016)
  • Author(s): 吉井健太郎
  • Organizer: 日本数学会2016 年度秋季総合 分科会
  • Place of Presentation: 関西大学(大阪府吹田市)
• [Presentation] Nonlocal solutions of hyperbolic type equations (2015)
  • Author(s): 吉井健太郎
  • Organizer: 作用素論セミナー
  • Place of Presentation: 京都大学数理解析研究所(京都府、京都市)
  • Year and Date: 2015-10-30
• [Presentation] Nonlocal solutions of hyperbolic type equations (2015)
  • Author(s): 吉井健太郎
  • Organizer: 日本数学会2015 年度秋季総合分科会
  • Place of Presentation: 京都産業大学(京都府、京都市)
  • Year and Date: 2015-09-16
• [Presentation] On the abstract evolution equations of hyperbolic type (2015)
  • Author(s): 吉井健太郎
  • Organizer: ICCNODEA
  • Place of Presentation: Cluj-Napoca(ルーマニア)
  • Year and Date: 2015-07-16
  • Int'l Joint Research
• [Presentation] Nonlocal solutions of hyperbolic type equations (2015)
  • Author(s): 吉井健太郎
  • Organizer: Equadiff 2015
  • Place of Presentation: Lyon(フランス)
  • Year and Date: 2015-07-07
  • Int'l Joint Research
• [Presentation] On the abstract evolution equations of hyperbolic type (2015)
  • Author(s): 吉井健太郎
  • Organizer: SeminariDMI 2015
  • Place of Presentation: Perugia(イタリア)
  • Year and Date: 2015-05-19
  • Invited
• [Remarks] 東京理科大学 研究者情報データベース RIDAI
  • URL: https://www.tus.ac.jp/ridai/doc/ji/RIJIA01.php