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The research of caloric morphism

Research Project

Project/Area Number 19540161
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  Ibaraki University, 理学部, 准教授 (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)
鈴木 紀明  名古屋大学, 多元数理科学研究科, 准教授 (50154563)
Co-Investigator(Renkei-kenkyūsha) SUZUKI Noriaki  名城大学, 理工学部, 教授 (50154563)
Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywords熱方程式の解を保つ変換 / caloric morphism / Appell変換 / 熱方程式
Research Abstract

温度分布の変化を表す方程式は熱方程式と呼ばれ、物理学に由来し数学においても極めて重要である。この研究では、どちらも回転面状に曲がった二つの空間の上で、ある場所での熱方程式の解を別の場所での熱方程式の解に移す変換を具体的に調べ、中核となる変換の形を完全に決定した。一方、今後の進展に必要となる、曲がっていない空間上の波動方程式の解に対する変換についても調べ、3次元以上で変換の形を完全に決定した。

Report

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

    (25 results)

All 2009 2008 2007 Other

All Journal Article (13 results) (of which Peer Reviewed: 13 results) Presentation (10 results) Remarks (2 results)

  • [Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application2009

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

      Journal of Mathematics of Kyoto University (巻頁未定)(印刷中)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application2009

    • Author(s)
      安藤広
    • Journal Title

      Journal of Mathematics of Kyoto University (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Compact Toeplitz operators on parabolic Bergman spaces2008

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

      Hiroshima Mathematical Journal 38

      Pages: 177-192

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Interpolating sequences of parabolic Bergman spaces2008

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

      Potential Analysis 28

      Pages: 357-378

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008

    • Author(s)
      堀内利郎
    • Journal Title

      Kyungpook Mathematical Journal 48

      Pages: 15-24

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Compact Toeplitz operators on parabolic Bergman spaces2008

    • Author(s)
      西尾昌治
    • Journal Title

      Hiroshima Mathematical Journal 38

      Pages: 177-192

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Interpolating sequences of parabolic Bergman spaces2008

    • Author(s)
      西尾昌治
    • Journal Title

      Potential Analysis 28

      Pages: 357-378

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weighted Berezin transformations with application to the Toeplitz operators of Schatten class on the parabolic Bergman spaces2008

    • Author(s)
      西尾昌治
    • Journal Title

      Kodai Mathematical Journal 28

      Pages: 357-378

    • NAID

      130004687919

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008

    • Author(s)
      堀内利郎
    • Journal Title

      Kyungpook Mathematical Journal 48-1

      Pages: 15-24

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Compact Toeplitz operators on parabolic Bergman spaces.2008

    • Author(s)
      西尾昌治
    • Journal Title

      Hiroshima Mathematical Joumal 38(印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Toeplitz operators and Carleson measures on parabolic Bergman spaces.2007

    • Author(s)
      西尾昌治
    • Journal Title

      Hokkaido Mathematical Journal 36-1

      Pages: 563-583

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A conjugate system and tangential derivative norms on parabolic Bergman spaces

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

      Hokkaido Mathematical Journal (巻頁未定)(印刷中)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weighted Berezin transformations with application to the Toeplitz operators of Schatten class on the parabolic Bergman spaces

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

      Kodai Mathematical Journal (巻頁未定)(印刷中)

    • NAID

      130004687919

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Presentation] 放物型Bergman空間における指数1以下のSchatten族Toeplitz作用素の特徴付け2009

    • Author(s)
      西尾昌治、鈴木紀明、山田雅博
    • Organizer
      日本数学会2009年度年会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-28
    • Related Report
      2008 Final Research Report
  • [Presentation] Liouville type theorem associate with the wave equation2009

    • Author(s)
      下村勝孝
    • Organizer
      RIMS研究集会「ポテンシャル論とその関連分野」
    • Place of Presentation
      京都大学
    • Year and Date
      2009-02-18
    • Related Report
      2008 Final Research Report
  • [Presentation] Liouville type theorem associate with the wave equation2009

    • Author(s)
      下村勝孝
    • Organizer
      ポテンシャル論とその関連分野
    • Place of Presentation
      京都大学
    • Year and Date
      2009-02-18
    • Related Report
      2008 Annual Research Report
  • [Presentation] 異なる動径方向計量を持つ半ユークリッド空間の間の Caloric morphism2008

    • Author(s)
      下村勝孝
    • Organizer
      ポテンシャル論研究集会
    • Place of Presentation
      秋田大学
    • Year and Date
      2008-11-03
    • Related Report
      2008 Final Research Report
  • [Presentation] 異なる動径方向計量を持つ半ユークリッド空間の間のCaloric morphism2008

    • Author(s)
      下村勝孝
    • Organizer
      ポテンシャル論研究集会
    • Place of Presentation
      秋田大学
    • Year and Date
      2008-11-03
    • Related Report
      2008 Annual Research Report
  • [Presentation] On the Caffarelli-Kohn-Nirenberg inequalities involving Critical and Supercritical weights2008

    • Author(s)
      堀内利郎
    • Organizer
      日本数学会2008年度秋期総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Final Research Report
  • [Presentation] Toeplitz operators of Schatten class on parabolic Bergman spaces2008

    • Author(s)
      西尾昌治、鈴木紀明、山田雅博
    • Organizer
      日本数学会2008年度秋期総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Final Research Report
  • [Presentation] A conjugate system and tangential derivative norms on parabolic Bergman spaces2008

    • Author(s)
      西尾昌治、菱川洋介、山田雅博
    • Organizer
      日本数学会2008年度秋期総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Final Research Report
  • [Presentation] Carleson inequalities on parabolic Bergman spaces2008

    • Author(s)
      西尾昌治、鈴木紀明、山田雅博
    • Organizer
      2008年度日本数学会年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-24
    • Related Report
      2008 Final Research Report
  • [Presentation] Caloric morphism for rotation invariant metric on Euclidean spaces2007

    • Author(s)
      下村勝孝
    • Organizer
      Finland-Japan Joint Seminar on Analysis
    • Place of Presentation
      ヘルシンキ大学
    • Year and Date
      2007-08-29
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Remarks]

    • URL

      http://info.ibaraki.ac.jp/scripts/websearch/index.htm

    • Related Report
      2008 Annual Research Report
  • [Remarks] 茨城大学研究者情報総覧

    • URL

      http://info.ibaraki.ac.jp/scripts/websearch/index.htm

    • Related Report
      2007 Annual Research Report

URL: 

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

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