• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

The research of transformations which preserve the solutions of the heat equation and the wave equation.

Research Project

Project/Area Number 22540169
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionIbaraki University

Principal Investigator

SHIMOMURA Katsunori  茨城大学, 理学部, 教授 (00201559)

Co-Investigator(Kenkyū-buntansha) HORIUCHI Toshio  茨城大学, 理学部, 教授 (80157057)
NISHIO Masaharu  大阪市立大学, 理学研究科, 准教授 (90228156)
ANDO Hiroshi  茨城大学, 理学部, 講師 (60292471)
Co-Investigator(Renkei-kenkyūsha) SUZUKI Noriaki  名城大学, 理工学部, 教授 (50154563)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords熱方程式の解を保つ変換 / Appell変換 / 波動方程式の解を保つ変換 / ベイトマン変換 / caloric morphism / Bateman変換
Research Abstract

In this research, we studied the conformal mapping for general indefinite metric on semi-euclidean spaces, and the transformation which preserve the solutions of the associated hyperbolic equation. We determined the set of mappings and transformations, and also their explicit forms.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (23 results)

All 2013 2012 2011 2010

All Journal Article (17 results) (of which Peer Reviewed: 17 results) Presentation (6 results)

  • [Journal Article] Generalizations of Bateman's transformation for general indefinite metrics2013

    • Author(s)
      下村勝孝
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 45, (印刷中)

    • NAID

      130004949011

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Conjugate functions on spaces of parabolic Bloch type2013

    • Author(s)
      菱川洋介,西尾昌治,山田雅博
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 65 Pages: 487-520

    • NAID

      10031177289

    • URL

      http://projecteuclid.org/euclid.jmsj/1366896642

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Positive Toeplitz operators of finite rank on the parabolic Bergman spaces2013

    • Author(s)
      西尾昌治, 鈴木紀明, 山田雅博
    • Journal Title

      Kodai Mathematical Journal

      Volume: 36 Pages: 38-49

    • NAID

      130004496181

    • URL

      http://projecteuclid.org/euclid.kmj/1364562716

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generalizations of Bateman's transformation for general indefinite metrics2013

    • Author(s)
      Katsunori Shimomura
    • Journal Title

      Math. J. Ibaraki Univ.

      Volume: 45

    • NAID

      130004949011

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Peter Kumlin, On the Caffarelli-Kohn-Nirenberg-type inequalities involving critical and supercritical weights2012

    • Author(s)
      堀内利郎
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 52 Pages: 661-742

    • URL

      http://projecteuclid.org/euclid.kjm/1352987531

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application2012

    • Author(s)
      安藤広, 堀内利郎
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 52 Pages: 759-796

    • URL

      http://projecteuclid.org/euclid.kjm/1352987533

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A relation between the Lorentzian inversion and the Bateman transformation2012

    • Author(s)
      下村勝孝
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 44 Pages: 1-5

    • NAID

      130003373915

    • URL

      http://ir.lib.ibaraki.ac.jp/handle/10109/3540

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Schatten class Toeplitz operators on the parabolic Bergman space II2012

    • Author(s)
      西尾昌治, 鈴木紀明, 山田雅博
    • Journal Title

      Kodai Mathematical Journal

      Volume: 35 Pages: 52-77

    • NAID

      130004496158

    • URL

      http://projecteuclid.org/euclid.kmj/1333027254

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A relation between the Lorentzian inversion and the Bateman transformation2012

    • Author(s)
      Katsunori Shimomura
    • Journal Title

      Math. J. Ibaraki Univ.

      Volume: 44 Pages: 1-5

    • NAID

      130003373915

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A relation between the Lorentzian inversion and the Bateman transformation2012

    • Author(s)
      Katsunori Shimomura
    • Journal Title

      Math.J.Ibaraki Univ.

      Volume: (印刷中)

    • NAID

      130003373915

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Liouville type theorem associate with the wave equation2011

    • Author(s)
      下村勝孝
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 43 Pages: 51-64

    • NAID

      130001438930

    • URL

      http://ir.lib.ibaraki.ac.jp/handle/10109/2780

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Caloric morphisms between different radial metrics on semi-euclidean spaces of same dimension2011

    • Author(s)
      下村勝孝
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 43 Pages: 13-41

    • NAID

      130001438928

    • URL

      http://ir.lib.ibaraki.ac.jp/handle/10109/2778

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Liouville type theorem associate with the wave equation2011

    • Author(s)
      Katsunori Shimomura
    • Journal Title

      Math.J.Ibaraki Univ.

      Volume: 43 Pages: 51-64

    • NAID

      130001438930

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Caloric morphisms between different radial metrics on semi-euclidean spaces of same dimension2011

    • Author(s)
      Katsunori Shimomura
    • Journal Title

      Math.J.Ibaraki Univ.

      Volume: 43 Pages: 13-41

    • NAID

      130001438928

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Caloric morphisms between different radial metrics on semi-euclideanspaces of same dimension2011

    • Author(s)
      Katsunori Shimomura
    • Journal Title

      Math.J.Ibaraki Univ

      Volume: 43 Pages: 13-41

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Caloric Morphisms for rotation invariant metrics2010

    • Author(s)
      西尾昌治, 下村勝孝
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 43 Pages: 315-331

    • URL

      http://projecteuclid.org/euclid.hmj/1291818847

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Caloric morphism for rotation invariant metric2010

    • Author(s)
      Masaharu Nishio, Katsunori Shimomura
    • Journal Title

      Hiroshima Math.J.

      Volume: 40 Pages: 315-331

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Toeplitz operators on parabolic Bergman spaces2013

    • Author(s)
      西尾昌治
    • Organizer
      International Workshop on Potential Theory
    • Year and Date
      2013-02-04
    • Related Report
      2012 Final Research Report
  • [Presentation] 非正定値計量の等角写像について2011

    • Author(s)
      下村勝孝
    • Organizer
      2011年度ポテンシャル論研究集会
    • Year and Date
      2011-11-04
    • Related Report
      2012 Final Research Report
  • [Presentation] 放物型ベルグマン空間上のランク有限正定値Toeplitz作用素について2011

    • Author(s)
      西尾昌治, 鈴木紀明, 山田雅博
    • Organizer
      2011年度ポテンシャル論研究集会
    • Year and Date
      2011-11-04
    • Related Report
      2012 Final Research Report
  • [Presentation] A remark on conjugate system on parabolic Bergman spaces2010

    • Author(s)
      西尾昌治, 菱川洋介, 山田雅博
    • Organizer
      2010年度ポテンシャル論研究集会
    • Year and Date
      2010-11-07
    • Related Report
      2012 Final Research Report
  • [Presentation] 非正定値計量の等角写像に対するLiouville型の定理2010

    • Author(s)
      下村勝孝
    • Organizer
      2010年度ポテンシャル論研究集会
    • Year and Date
      2010-11-06
    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Presentation] 非正定値計量の等角写像について2010

    • Author(s)
      下村勝孝
    • Organizer
      2011年度ポテンシャル論研究集会
    • Place of Presentation
      岐阜大学
    • Year and Date
      2010-11-04
    • Related Report
      2011 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi