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Radon transforms on homogeneous spaces and their application to harmonic analysis

Research Project

Project/Area Number 19540208
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionUniversity of Tsukuba

Principal Investigator

KAKEHI Tomoyuki  University of Tsukuba, 大学院・数理物質科学研究科, 准教授 (70231248)

Co-Investigator(Kenkyū-buntansha) ISOZAKI Hiroshi  筑波大学, 大学院・数理物質科学研究科, 教授 (90111913)
TAKEUCHI Kiyoshi  筑波大学, 大学院・数理物質科学研究科, 准教授 (70281160)
KINOXHITA Tamotsu  筑波大学, 大学院・数理物質科学研究科, 准教授 (90301077)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsラドン変換 / 等質空間 / 対称空間 / 像の特徴付け / 反転公式 / シュレディンガー方程式 / 基本解 / 台 / 像の特徴づけ / 多重時間波動方程式
Research Abstract

We studied Radon transforms on homogeneous spaces, and their applications to harmonic analysis. Our results are as follows. (1) We proved that the ranges of generalized matrix Radon transforms are characterized by Pfaffian type invariant differential operators. In addition, we also obtained the inversion formulas. (2) We proved that under some condition the support of the fundamental solution to the Schroedinger equation on a compact symmetric space becomes a lower dimensional subset at a rational time and that it coincides with the whole symmetric space at an irrational time.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (9 results)

All 2009 2008 2007 Other

All Journal Article (5 results) (of which Peer Reviewed: 4 results) Presentation (4 results)

  • [Journal Article] Pseudodifferentialmulti-product representation of the solution operator of a parabolic equation2009

    • Author(s)
      Isozaki Hiroshi, Le Rousseau Jerome
    • Journal Title

      Comm.Partial Differential Equations 34, no. 7-9

      Pages: 625-655

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Topological Radon transforms and degree formulas for dual varieties2008

    • Author(s)
      Matsui Yutaka, Takeuchi Kiyoshi
    • Journal Title

      Proc.Amer.Math.Soc. 136, no.7

      Pages: 2365-2373

    • NAID

      120007138843

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Cauchy problem for wave equations with time-dependent coefficients2008

    • Author(s)
      Kinoshita Tamotu, Yagdjian Karen
    • Journal Title

      Int.J.Appl.Math.Stat. 13, No. S08

      Pages: 1-20

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Uhlmann Gunter Probing for electrical inclusions with complex spherical waves2007

    • Author(s)
      Ide Takanori, Isozaki Hiroshi, Nakata Susumu, Siltanen Samuli
    • Journal Title

      Comm.Pure Appl.Math. 60, no. 10

      Pages: 1415-1442

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Fundamental solution to the Schroedinger equation on a compact symmetric space

    • Author(s)
      Kakehi Tomoyuki
    • Journal Title

      数理解析研究所講究録 (掲載確定)

    • Related Report
      2009 Final Research Report
  • [Presentation] 「Generalized Matrix Radon transform」 Workshop on Integral Geometry and Group Representations2009

    • Author(s)
      Kakehi Tomoyuki
    • Organizer
      Tambara Institute of mathematical Sciences
    • Place of Presentation
      the University of Tokyo (Tambara, Numata, Gumma)
    • Related Report
      2009 Final Research Report
  • [Presentation] Fundamental solution to the Schroedinger equation on a compact symmetric space2008

    • Author(s)
      筧 知之
    • Organizer
      アメリカ数学会
    • Place of Presentation
      ルイジアナ州立大学
    • Year and Date
      2008-03-28
    • Related Report
      2007 Annual Research Report
  • [Presentation] Fundamental solution to the Schroedinger equation on a compact symmetric space2008

    • Author(s)
      Kakehi Tomoyuki
    • Organizer
      Special Session on Radon Transforms, Tomography, and Related Geometric Analysis 2008 AMS Spring Southeastern Meeting (AMS Sectional Meeting)
    • Place of Presentation
      Louisiana State University, Baton Rouge, USA
    • Related Report
      2009 Final Research Report
  • [Presentation] Some remarks on the Schroedinger equation on compact symmetric spaces2007

    • Author(s)
      Kakehi Tomoyuki
    • Organizer
      International Conference on Integral Geometry, Harmonic Analysis and Representation Theory
    • Place of Presentation
      University of Iceland, Natural Sciences Building, Reykjavik, Iceland
    • Related Report
      2009 Final Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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