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Study of algebraic structure and geometric structure of Schroedinger equations on symmetric spaces

Research Project

Project/Area Number 23540243
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Global analysis
Research InstitutionOkayama University

Principal Investigator

KAKEHI Tomoyuki  岡山大学, 自然科学研究科, 教授 (70231248)

Co-Investigator(Kenkyū-buntansha) TAMURA Hideo  岡山大学, 自然科学研究科, 名誉教授 (30022734)
Co-Investigator(Renkei-kenkyūsha) YAMADA Hirofumi  岡山大学, 自然科学研究科, 教授 (40192794)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywordsシュレディンガー方程式 / 対称空間 / 基本解 / 磁場 / ガウス和 / コンパクト対称空間 / 特異性 / 台 / 特異台 / 零エネルギー条件
Research Abstract

We mainly studied the detailed structure of the fundamental solution to the Schroedinger equation on compact symmetric spaces from the point of view of number theory and representation theory. One of our main results is as follows. Under certain assumptions on the vector potential and on compact symmetric spaces, the singular support of the fundamental solution to the magnetic Schroedinger equation becomes a lower dimensional subset of the compact symmetric space, which is given in terms of generalized Gauss sums at a rational time. On the other hand, at an irrational time, the singular support of the fundamental solution coincides with the whole symmetric space.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (21 results)

All 2014 2013 2012 2011 Other

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (18 results) (of which Invited: 13 results)

  • [Journal Article] Resonances in scattering by two magnetic fields at large separation and a complex scaling method2014

    • Author(s)
      Ivana Alexandrova and Hideo Tamura
    • Journal Title

      Adv. Math.

      Volume: 256 Pages: 398-448

    • DOI

      10.1016/j.aim.2014.01.022

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Magnetic Schroedinger equation on compact symmetric spaces and the geodesic Radon transform of one forms2013

    • Author(s)
      Tomoyuki Kakehi
    • Journal Title

      Contemporary Mathematics

      Volume: 598 巻 Pages: 129-138

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Support theorem for the fundamental solution to the Schrodinger equation on certain compact symmetric spaces2011

    • Author(s)
      T.Kakehi
    • Journal Title

      Adv.Math.

      Volume: 226 Issue: 3 Pages: 2739-2763

    • DOI

      10.1016/j.aim.2010.10.003

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Schroedinger equation on compact symmetric spaces and reciprocity for Gauss sums2014

    • Author(s)
      筧 知之
    • Organizer
      Geometric and Singular Analysis
    • Place of Presentation
      Potsdam University (Germany)
    • Year and Date
      2014-03-24
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Schrödinger equation on compact symmetric spaces and reciprocity for Gauss sums2014

    • Author(s)
      Tomoyuki Kakehi
    • Organizer
      Geometric and Singular Analysis
    • Place of Presentation
      Potsdam University (Germany)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] L2-wellposedness for Schroedinger type equations on compact symmetric spaces2013

    • Author(s)
      筧 知之
    • Organizer
      The 20th Microlocal Analysis and Classical Analysis
    • Place of Presentation
      京都大学理学研究科セミナーハウス
    • Year and Date
      2013-11-22
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Magnetic Schroedinger equation on compact symmetric spaces, Analysis, Geometry and Group Representations for Homogeneous Spaces2013

    • Author(s)
      筧 知之
    • Organizer
      JSPS-NWO Seminar
    • Place of Presentation
      名古屋大学理学部
    • Year and Date
      2013-08-28
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Magnetic Schroedinger equation on compact symmetric spaces2013

    • Author(s)
      Tomoyuki Kakehi
    • Organizer
      Analysis, Geometry and Group Representations for Homogeneous Spaces, JSPS-NWO Seminar
    • Place of Presentation
      名古屋大学理学部
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Schrödinger equation on compact symmetric spaces and reciprocity for Gauss sums2013

    • Author(s)
      Tomoyuki Kakehi
    • Organizer
      Functional Analysis and Global Analysis
    • Place of Presentation
      東京理科大学理工学部
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] L2-wellposedness for Schrödinger type equations on compact symmetric spaces2013

    • Author(s)
      Tomoyuki Kakehi
    • Organizer
      The 20th Microlocal Analysis and Classical Analysis
    • Place of Presentation
      京都大学理学研究科セミナーハウス
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On the support of the fundamental solution to the Schroedinger equation on certain compact symmetric spaces2012

    • Author(s)
      筧 知之
    • Organizer
      Functional Analysis and Global Analysis
    • Place of Presentation
      東京理科大学理工学部
    • Year and Date
      2012-11-19
    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Invited
  • [Presentation] Schroedinger equation on certain compact symmetric spaces2012

    • Author(s)
      筧 知之
    • Organizer
      AMS Special Session on Radon Transforms and Geometric Analysis
    • Place of Presentation
      Hynes Convention Center, Boston, USA
    • Year and Date
      2012-01-07
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Magnetic Schroedinger equation on compact symmetric spaces2012

    • Author(s)
      Tomoyuki Kakehi
    • Organizer
      第102回神楽坂解析セミナー
    • Place of Presentation
      東京理科大学理学部
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] コンパクト対称空間上の磁場付きシュレディンガー方程式について2012

    • Author(s)
      Tomoyuki Kakehi
    • Organizer
      大阪市立大学複素解析セミナー
    • Place of Presentation
      大阪市立大学数学研究所
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Fundamental solution to the Schroedinger equation on compact symmetric spaces and Gauss sums2011

    • Author(s)
      筧 知之
    • Organizer
      微分方程式の総合的研究
    • Place of Presentation
      東京大学
    • Year and Date
      2011-12-18
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] コンパクト対称空間上のシュレディンガー方程式の基本解とガウス和2011

    • Author(s)
      筧 知之
    • Organizer
      日本数学会秋季分科会関数解析分科会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-28
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Fundamental solution to the Schoedinger equation on certain compact symmetric spaces2011

    • Author(s)
      筧 知之
    • Organizer
      Nonlinear Dynamics in Partial Differential Equations
    • Place of Presentation
      九州大学
    • Year and Date
      2011-09-19
    • Related Report
      2013 Final Research Report
  • [Presentation] コンパクト対称空間上のシュレディンガー方程式の基本解とガウス和

    • Author(s)
      筧 知之
    • Organizer
      日本数学会秋季分科会関数解析分科会(招待講演)
    • Place of Presentation
      信州大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Schroedinger equation on certain compact symmetric spaces

    • Author(s)
      Tomoyuki Kakehi
    • Organizer
      AMS Special Session on Radon Transforms and Geometric Analysis(招待講演)
    • Place of Presentation
      Hynes Convention Center, Boston, USA
    • Related Report
      2011 Research-status Report
  • [Presentation] Fundamental solution to the Schroedinger equation on compact symmetric spaces and Gauss sums

    • Author(s)
      筧 知之
    • Organizer
      微分方程式の総合的研究(招待講演)
    • Place of Presentation
      東京大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Fundamental solution to the Schoedinger equation on certain compact symmetric spaces

    • Author(s)
      Tomoyuki Kakehi
    • Organizer
      Nonlinear Dynamics in Partial Differential Equations(招待講演)
    • Place of Presentation
      九州大学
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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