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STUDIES ON BEHAVIORS OF SOLUTIONS DIFFERENTIAL EQUATIONS

Research Project

Project/Area Number 12640208
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionKYOTO INSTITUTE OF TECHNOLOGY

Principal Investigator

UCHIYAMA Jun  KYOTO INSTITUTE OF TECHNOLOGY, FACULTY OF TEXTILE SCIENCE, PROFESSOR, 繊維学部, 教授 (70025401)

Co-Investigator(Kenkyū-buntansha) MAITANI Fumio  KYOTO INSTITUTE OF TECHNOLOGY, FACULTY OF ENGINEERING AND DESIGN, PROFESSOR, 工芸学部, 教授 (10029340)
NAKAOKA Akira  KYOTO INSTITUTE OF TECHNOLOGY, FACULTY OF ENGINEERING AND DESIGN, PROFESSOR, 工芸学部, 教授 (90027920)
IWATSUKA Akira  KYOTO INSTITUTE OF TECHNOLOGY, FACULTY OF TEXTILE SCIENCE, PROFESSOR, 繊維学部, 教授 (40184890)
YAGASAKI Tatuhiko  KYOTO INSTITUTE OF TECHNOLOGY, FACULTY OF ANGINEERING AND DESIGN, ASSOCIATE PROFESSOR, 工芸学部, 助教授 (40191077)
OKURA Hiroyuki  KYOTO INSTITUTE OF TECHNOLOGY, FACULTY OF ENGINEERING ANDDESIGN, ASSOCIATE PROFESSOR, 工芸学部, 助教授 (80135649)
Project Period (FY) 2000 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2001: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2000: ¥900,000 (Direct Cost: ¥900,000)
Keywordssolutions of differential equations / schrodinger operator / neumann-wiegner potentials / positive eigenvalue / growth order of eigenfunctions / 微分方程式 / Neumann-Wiegner / 固有関数 / 解の増大度 / 量子力学 / 極限吸収原理 / Meumann-Wiegnerポテンシャル / 唯一接続定理
Research Abstract

I, the head investigator of our project "Studies on behaviors of solutions of differential equations", participated in many symposia or workshops held the period April, 2000 to March, 2003 such as
"The summer symposium on operator theory"
"The symposium on differential equations"
which were held each year. And I received many informations related to our project from there and I reported our results related to our projects.
In the "Memorial Symposium for Professor Nobuhisa on Partial Differential Equations" held at Kyoto (2001/1/22-1/25), I, with Masaharu Arai, gave a lecture titled "Positive Eigenvalues of the Schrodinger Operators having von Neumann-Wiegner Potentials".
I also gave lectures titled "Growth Order of Eigenfunctions of the Schodinger Operators having von Neumann-Wiegner Potentials" in the
"The seminar on partial differential equatins, Chu-oh Univ. (Tokyo) (2003/5/28-5/29)"
"The summer symposium on operator theory (Miyazaki) (2003/9/5-9/8)"
All other investigators associated on our project partipated to many symposia respectively, and recognized the problems which are related in the behaviors of solutions of differential equations. Their results are reported in the "Reports of research project, grant-in-aid for scientific research, Studies on Behaviors of Solutions of Differential Equations".

Report

(5 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • 2000 Annual Research Report

Research Products

(69 results)

All Other

All Publications

  • [Publications] 荒井 正治: "von Neumann-Wiegner型ポテンシャルの正の固有値"岩崎敷久教授記念偏微分方程式研究集会予稿集. 85-94 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Akira Iwatsuka: "The uniqueness of the integrated density of states for the Schrodinger operators with magnetic fields"Mathematische Zeitschrift. 237-2. 335-371 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Akira Nakaoka: "Une methode pour construction de fonction d'echelle d'ondelettes du rang M"Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology. 48. 1-9 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Akira Nakaoka: "Solution non-negative pour quelque equation fonctionelle"Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology. 49. 1-18 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Akira Nakaoka: "A method for construction of wavelet systems"Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology. 52. (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Fumio Maitani: "Ahlfors-Rauch type variational formulas on complex manifolds"Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology. 49. 19-36 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Ishida: "Conformal imbeddings of Denjoy domains"Acta Human.Sci.Univ.Sangio Kyotiensis. 30. 1-7 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Fumio Maitani: "Smoothness of rank M scaling functions"Applied and Computational Harmonic Analysis. 13. 116-137 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Ishida: "Conformal imbeddings of Denjoy domains II"Acta Human.Sci.Univ.Sangio Kyotiensis. 31. 1-5 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroshi Yamaguchi: "Period reproducing forms and extremal length"Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology. 52. 19-36 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyuki Okura: "On large deviation theorems for Markov processes on a compact domain"Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology. 48. 11-22 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 大倉弘之: "直交M進ウェーブレットのなめらかさについて"統計数理研究所共同研究レポート 逆問題とその周辺(6). 128. 57-72 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyuki Okura: "Recurrence and transience criteria for subordinated symmetric Markov processes"Forum Math.. 14. 121-146 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 大倉弘之: "容量不等式と再帰性の判定"数理解析研究所講究録「ポテンシャル論とその周辺」. 1293. 132-143 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyuki Okura: "Capacitary upper estimates for symmetric Dirichlet forms"Potential Anal.. 19. 211-235 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tatsuhiko Yagasaki: "Spaces of embeddings of comapct polyhedra into 2-manifolds"Topology Appl.. 108. 107-122 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tatsuhiko Yagasaki: "Homotopy types of homeomorphism groups of noncompact 2-manifolds"Topology Appl.. 108. 123-136 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tatsuhiko Yagasaki: "Hyperspaces of Peano and ANR continua"Topology Appl.. 113. 309-320 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tatsuhiko Yagasaki: "Embedding spaces and hyperspaces of polyhedra in 2-manifolds"Topology Appl.. 121. 247-254 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tatsuhiko Yagasaki: "The groups of PL and Lipschitz homeomorphisms of noncompact 2-manifolds"Bulletin of the Polish Academy of Sciences, Mathematics. 51(4). 445-466 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tatsuhiko Yagasaki: "Homotopy types of the components of spaces of embeddings of compact polyhedra into 2-manifolds"Topology Appl.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mamoru Asada: "The compatibility of the filtration of mapping class groups of two surfaces pasted along the boundaries"Topology Appl.. 108. 217-232 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mamoru Asada: "The faithfulness of the monodromy representations associated with certain families of algebraic curves"Journal of Pure ana Applied Algebra. 159. 123-147 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mamoru Asada: "On centerfree quotients of surface groups"Communications in algebra. 29(7). 2871-2875 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 石田久: "ヴィジュアル複素解析"培風館. (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Arai: "Positive eigenvalues of the Schrodinger operators having von Neumann-Wiegner potentials (in Japanese)"Proceedings of Memorial Symposium for Professor Nobuhisa Iwasaki on Partial Differential Equations. 85-94 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Iwatsuka: "The uniqueness of the integrated density of states for the Schrodinger operators with magnetic fields"Mathematische Zeitschrift. 237-2. 335-371 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Nakaoka: "Une methode poer construction de fonction d'echelle d'ondelettes du rang M"Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology. 48. 1-9 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Nakaoka: "Solution non-negative pour quelque equation fonctionelle"Memoirs of the Faculty of Engineering and Design, Kyoto of Institute of Technology. 49. 1-9 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Nakaoka: "A method for construction of wavelet systems"Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology. 52. (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] F.Maitani: "Ahlfors-Rauch type variation formulas on complex manifolds"Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology. 49. 19-36 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Ishida: "Conformal imbeddings of Denjoy domains"Acta Human. Sci. Univ. Sangio Kyotiensis. 30. 1-7 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] F.Maitani: "Smoothness of rank M scaling functions"Applied and Computational Harmonic Analysis. 13. 116-137 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.ishida: "Conformal imbeddings of Denjoy domains II"Acta Human. Sci. Univ. Sangio Kyotiensis. 31. 1-5 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Yamaguchi: "Period reproducing forms and extremal length"Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology. 52. 19-36 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Okura: "On large deviation theorems for Markov processes on a compact domain"Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology. 48. 11-22 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Okura: "Smoothness of orthogonal rank M wavelets (in Japanese)"Cooperative research reports, the institute of statiscal mathematics, inverse problems and related topics (6). 128. 57-72 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Okura: "Recurrence and transience criteria for subordinated symmetric Markov processes"Forum Math. 14. 121-146 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Okura: "Capacity inequality and recurrence criteria (in Japanese)"Suurikaisekikenkyuujko koukyuuroku, Potential theory and related topics. 1293. 132-143 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Okura: "Capacitary upper estimated for symmetric Dirichlet forms"Potential Anal.. 19. 211-235 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.YAgasaki: "Spaces of embeddings of comapct polyhedra into 2-manifolds"Topology Appl.. 108. 107-122 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Yagasaki: "Homotopy types of homeomorphism groups of noncompact 2-manifolds"Topology Appl.. 108. 123-136 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Yagasaki: "Hyperspaces of Peano and ANR continua"Topology Appl.. 113. 309-320 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Yagasaki: "Embedding spaces and hyperspaces of polyhedra in 2-manifolds"Topology Appl.. 121. 247-254 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Yagasaki: "The groups of PL and Lipschitz homeomorphisms of noncompact 2-manifolds"Bulletin of the Polish Academy of Sciences, Mathematics. 51(4). 445-466 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Yagasaki: "Homotopy types of the components of spaces of embedding of compact polyhedra into 2-manifolds"Topology Appl.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.asada: "The compatibility of the filtration of mapping class groups of two surfaces pasted along the boundaries"Topology Appl.. 108. 217-232 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Asada: "The faithfulness of the monodromy representations associated with certain families of algebraic curves"Journal of Pure ana Applied Algebra. 159. 123-147 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Asada: "On centerfree quotients of surface groups"Communications in algebra. 29(7). 2871-2875 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Akira Nakaoka: "A method for construction of wavelet systems"Memoirs of the Faculty of Engineering and Design, KIT. 52. (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hiroyuki Okura: "Capacitary upper estimates for symmetric Dirichlet forms"Potential Anal.. 19. 211-235 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Tatsuhiko Yagasaki: "The groups of PL and Lipschitz homeomorphisms of noncompact 2-manifolds"Bulletin of the Polish Academy of Sciences, Mathematics. 51(4). 445-466 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Fumio Maitani: "Smoothness of rank M scaling functions"Appl. Comput. Harmon. Anal.. 13. 116-137 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Hisashi Ishida: "Conformal imbeddings of Denjoy domains II"Acta Human. Sci. Univ. Sangio Kyotiensis. 31. 1-5 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Hiroyuki Okura: "Capacitary upper estimates for symmetric Dirichlet forms"Potential Anal.. (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] 大倉 弘之: "容量不等式と再帰性の判定"数理解析研究所講究録「ポテンシャル論とその周辺」. 1293. 132-143 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Tatsuhiko Yagasaki: "Embedding spaces and hyperspaces of polyhedra in 2-manifolds"Topology Appl.. 121. 247-254 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 荒井 正治: "von Neumann-Wiegner型ポテンシャルの正の固有値"岩崎敷久教授記念偏微分方程式研究集会予稿集. 85-94 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] A.Iwatsuka: "The uniqueness of the integrated density of states for the Schrodinger operators with magnetic fields"Mathematische Zeitschrift. 237・2. 335-371 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] A.Nakaoka: "Solution non-negative pour quelque equation fonctionelle"Mem.Fac.Eng.and Design Kyoto Inst.Tech.. 49. 1-18 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] F.Maitani: "Ahlfors-Rauch Type Variational Formulas on Complex Manifolds"Mem.Fac.Eng.and Design Kyoto Inst.Tech.. 49. 19-36 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Okura: "Recurrence and transience criteria for subordinated symmetric Markov processes"Forum Math. (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Yagasaki: "Hyperspaces of Peano and ANR continua"Topology Appl.. 113. 309-320 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 荒井正治: "von Neumann-Wiegner型ポテンシャルの正の固有値"岩崎敷久教授記念偏微分方程式研究集会予稿集. 85-94 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Doi: "The uniqueness of the integrated density of states for the Schrodinger operators with magnetic fields"Mathematische Zeitschrift. (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] A.Nakaoka: "Une methode pour construction de fonction d'echelle d'ondelettes du rang M"Mem.Fac.Eng.and Design Kyoto Inst.Tech.. 48. 1-9 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] F.Maitani: "Ahlfors-Rauch Type Variational Formulas on Complex Manifolds"Mem.Fac.Engi.Des.Kyoto Inst.Tech.. 49. 17-38 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Okura: "On large deviation theorems for Markov processes on a compact domain"Mem.Fac.Engi.Des.Kyoto Inst.Tech.. 48. 11-22 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Yagasaki: "Spaces of embeddings of compact polyhedra into 2-manifolds"Topology Appl.. 108. 107-122 (2000)

    • Related Report
      2000 Annual Research Report

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Published: 2000-03-31   Modified: 2016-04-21  

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