Inverse scattering problems for singular rank-one perturbations of a selfadjoint operator

• Project/Area Number: 23540219
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: YOSHITOMI Kazushi 首都大学東京, 理工学研究科, 准教授 (40304729)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 散乱逆問題 / 自己共役作用素 / 特異ランク1摂動 / 特異摂動 / 特異ランク１摂動 / 点相互作用 / 国際研究者交流 / バルセロナ（スペイン）

Research Abstract

One of the most important problems in the scattering theory is the characterization of the scattering matrices. This investigation studies forward and inverse scattering problems for singular rank-one perturbations of a selfadjoint operator A. I obtain necessary and sufficient conditions for a function to be the phase shift of a singular rank-one perturbation of A. This result is closely related with the theory of point interactions.

Research Products

• [Journal Article] Inverse scattering problems for singular rank-one perturbations of a selfadjoint operator (2012)
  • Author(s): Kazushi Yoshitomi
  • Journal Title: Asymptotic Analysis Volume: 80 Pages: 213-221
• [Journal Article] A remark on double singular integrals (2012)
  • Author(s): Kazushi Yoshitomi
  • Journal Title: Kyushu Journal of Mathematics Volume: 66 Pages: 429-433
  • NAID: 130002543085
• [Journal Article] Inverse scattering problems for singular rank-one perturbations of a self-adjoint operator (2012)
  • Author(s): Kazushi Yoshitomi
  • Journal Title: Asymptotic Analysis Volume: 80 Issue: 3-4 Pages: 213-221
  • DOI: 10.3233/asy-2012-1112
  • Peer Reviewed
• [Presentation] A uniform coerciveness result for biharmonic operator and its application to a parabolic equation (2013)
  • Author(s): 吉冨和志
  • Organizer: 数理工学数学談話会
  • Place of Presentation: 大阪府立大学
  • Year and Date: 2013-12-06
• [Presentation] A uniform coerciveness result for biharmonic operator and its application to a parabolic equation (2013)
  • Author(s): 吉冨和志
  • Organizer: 月曜解析セミナー
  • Place of Presentation: 北海道大学
  • Year and Date: 2013-10-28
• [Presentation] A uniform coerciveness result for biharmonic operator and its application to a parabolic equation (2013)
  • Author(s): 吉冨和志
  • Organizer: 月曜解析セミナー
  • Place of Presentation: 北海道大学理学部
• [Presentation] A uniform coerciveness result for biharmonic operator and its application to a parabolic equation (2013)
  • Author(s): 吉冨和志
  • Organizer: 数理工学数学談話会
  • Place of Presentation: 大阪府立大学工学部