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Problems in Global Analysis

Research Project

Project/Area Number 01460003
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionTohoku University

Principal Investigator

KOTAKE Takeshi  Tohoku Univ., Maths. Inst., Prof., 理学部, 教授 (30004427)

Co-Investigator(Kenkyū-buntansha) ARAI Hitoshi  Tohoku Univ., Maths. Inst., Lecturer, 理学部, 講師 (10175953)
BANDO Shigetoshi  Tohoku Univ., Maths. Inst., Assoc. Prof., 理学部, 助教授 (40165064)
ITO Hidekazu  Tohoku Univ., Maths. Inst., Assoc. Prof., 理学部, 助教授 (90159905)
TAKAGI Izumi  Tohoku Univ., Maths. Inst., Assoc. Prof., 理学部, 助教授 (40154744)
KATO Junji  Tohoku Univ., Maths. Inst., Prof., 理学部, 教授 (80004290)
小野 薫  東北大学, 理学部, 助手 (20204232)
Project Period (FY) 1989 – 1990
Project Status Completed (Fiscal Year 1990)
Budget Amount *help
¥4,600,000 (Direct Cost: ¥4,600,000)
Fiscal Year 1990: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1989: ¥2,700,000 (Direct Cost: ¥2,700,000)
KeywordsSchrodinger operator / Dirac operator / integrable hamiltonian system / functional differential equation / harmonic function / Bergman kernel / シュレディンガ-方程式 / ハミルトン力学系 / 調和関数 / バ-グマン核 / 周期的シュレ-ディンガ-方程式 / ヤン・ミルズ汎函数 / 半線型楕円型方程式 / ハミルトンベクトル場 / バ-コフ標準型 / ハ-ディ空間 / ケ-ラ-多様体 / トレリの問題
Research Abstract

The research had the purpose of contributing to the cross-fertilisation of analysis and geometry, through the development of global analysis on manifolds, and exploring at the same time interesting and potentially fruitful interrelations between various fields of mathematics.
The project involved work in partial differential equations, dynamical systems, harmonic analysis and other diverse topics in analysis.
The results obtained during the period of this research project can be summarised as follows.
1. Partial differential equations and their applications to geometry : (1) study of asymptotic distribution of eigenvalues for Schrodinger operators with non-classical positive potentials ; (2) study of equivariant index of Dirac operators on spin manifolds ; (3) proof of the removability of isolated singularities for holomorphic vector bundles in connection with their Ricci curvature.
2. Dynamical system and functional differential equations : (1) reduction of integrable hamiltonian system to the normal form near singular points ; (2) discovery of various criteria for the existence and stability of functional differential equations with infinite delay.
3. Nonlinear analysis : (1) study on geometric structures of solutions, such as pattern formation and the appearance of singularities for reaction-diffusion equations ; (2) proof of asymptotic stability of gradient flow, associated with the Yang-Mills functional.
4. Harmonic analysis and operator theory : (1) proof of a Fatou-type theorem concerning the boundary behavior of harmonic functions on strictly pseudo-convex domains ; (2) study on the interrelation between the order structure and the regular completion of operator algebras.
5. Analysis on complex manifolds : study on the Bergman kernels on strictly pseudo-convex Reinhardt domains in C^2 in connection with the Chern-Moser invariant polynomials of the boundaries.

Report

(3 results)
  • 1990 Annual Research Report   Final Research Report Summary
  • 1989 Annual Research Report
  • Research Products

    (54 results)

All Other

All Publications (54 results)

  • [Publications] 新井 仁之: "Boundary behavior of function on complete manifolds of negative curvature" Tohoku Math.J.41. 307-319 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 新井 仁之: "Estimates of harmonic measres associated with degenerate Laplacian on strictly pseudoconvex domains" Proc.Japan Acad.66. 13-15 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 伊藤 秀一: "Convergence of Birkhoff normal forms for integrable systems" Comment.Math.Helv.64. 412-461 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 伊藤 秀一: "On the holonomy group associated with analytic continuations of solutions for integrable systems" Bol.Soc.Breas.Mat.21. 95-120 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 小野 薫: "Equivariant index of Dirac operators" Tohoku Math.J.42. 319-332 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 加藤 順一: "Compact boundedness in periodic functional defferential equations with infinite delay" Proc.Royal Soc.Edinburgh. 114. 291-297 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 中澤 則之: "Asymptotic Expansion of the Bergman Kernel for Strictly Pseudoconvex Complete Reinhardt Domains in C^2" Proc.Japan Acad.66. 39-41 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 板東 重稔: "Removable singularities for holomorphic vector bundles" Tohoku Math. J.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] ARAI, Hitoshi :"Boundary behavior of functions on complete manifolds of negative curvature." Tohoku Math. J.Vol. 41. 307-319 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] ARAI, Hitoshi :"Estimates of harmonic measures associated with degenerate Laplacian on strictly pseudoconvex domains." Proc. Japan Acad.Vol. 66. 13-15 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] BANDO, Shigetoshi :"Bubbling out of Einstein manifolds." Tohoku Math. J.Vol. 42. 175-180 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] BANDO, Shigetoshi :"Removable singularities for holomorphic vector bundles." Tohoku Math. J.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] HORIHATA, Kazuhiro :"Pointwise property of L^P-functions with Nikoski condition" Boll. Unione Mat. Italiana. Vol. 7. 199-207 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] ITO, Hidekazu :"Convergence of Birkhoff normal forms for integrable systems." Comment. Math. Helv.Vol. 64. 412-461 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] ITO, Hidekazu :"On the holonomy group associated with analytic continuation of solutions for integrable systems." Bol. Soc. Bras. Mat.Vol. 21. 95-120 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] KATO, Junji :"Compact boundedness in periodic functional differential equations with infinite delay." Proc. Royal Soc. Edinburgh. Vol. 114. 291-297 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] KONNO, Kazuhiro :"Generic Torelli theorem for hypersurfaces of certain compact homogeneous Kahler manifolds." Duke Math. J.Vol. 59. 83-160 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] NAGASAWA, Takeyuki :"Asymptotical stability of Yang-Mills' gradient flow." Geometry of Manifolds Academic Press. 499-517 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] NAGASAWA, Takeyuki: "Uniqueness and Widder's theorems for the heat equation on Riemannian manifolds." Preprint.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] NAKAZAWA, Noriyuki: "Asymptotic expansion of the Bergman kernel for strictly pseudoconvex complete Reinhardt domains in C^2." Proc. Japan Acad.Vol. 66. 39-41 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] ONO, Kaoru :"Equivariant index of Dirac operators." Tohoku Math. J.Vol. 42. 319-332 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] SAITO, Kazuyuki :"Embeddable AW^*-algebras and regular completions." J. London Math. Soc.Vol. 34. 511-523 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] TACHIZAWA, Kazuya :"Asymptotic distribution of eigenvalues of Schrodinger operators with non-classical potentials." Tohoku Math. J.Vol. 42. 381-406 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] TACHIZAWA, Kazuya :"Eigenvalue asymptotics of Schrodinger operators with positive potentials." Tohoku Math. J.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] TAKAGI, Izumi :"On the shape of least-energy solutions to a semi-linear Neumann problem. (First author : W. M. Ni)" Comm. Pure and Appl. Math.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 新井 仁之: "Estimates of harmonic measures associated with degenerate Laplacian on strictly pseudoconvex domains" Proc.Japan Acad.66. 13-15 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 伊藤 秀一: "On the holonomy group associated with analytic continuations of solutions for integrable systems" Bol.Soc.Bras.Mat. 21. 95-120 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 加藤 順二: "Compact boundedness in periodic functional differential equations with infinite delay" Proc.Royal Soc.Edinburgh. 114. 291-297 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 斎藤 和之: "Embeddable AW^*ーalgebras and regular completions" J.London Math.Soc.34. 511-523 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 立沢 一哉: "Asymptotic distribution of eigenvalues of Schro^^¨dinger operators with nonーClassical potentials" Tohoku Math.J.42. 381-406 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 高木 泉 (第一著者,W.N.Ni): "On the shape of leastーenergy solutions to a semilinear Neumann problem" Comm.Pure and Applied Math.

    • Related Report
      1990 Annual Research Report
  • [Publications] 今野 一宏: "Generic Torelli theorem for hypersurfaces of certain compact homogeneous Ka^^¨hler manifolds" Duke Math.J.59. 83-160 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 斎藤 和之: "Embeddable AW^*ーalgebras and regular eompletions" J.London Math.Soc.34. 511-523 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 立沢 一哉: "Asymptotic distribution of eigenvalues of Schro^^¨dinger oprators with non classical potentials" Tohoku Math.J.42. 381-406 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 立沢 一哉: "Eigenvalue asymptotics of Schro^^¨dinger oprators with positive potentials" Tohoku Math.J.

    • Related Report
      1990 Annual Research Report
  • [Publications] 高木 泉 (第一著者,W.N.Ni): "On the shape of least energy solutions to a semilinear Neumann problem" Comm.Pure and Applied Math.

    • Related Report
      1990 Annual Research Report
  • [Publications] 長澤 壮之: "Asymptotical stability of YangーMills' gradient flow" “Geometry of Manifolds." Academic press. 499-517 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 長澤 壮之: "Uniqueness and Widder's theorems for the heat equation on Riemannian manifolds" preprint.

    • Related Report
      1990 Annual Research Report
  • [Publications] 中澤 則之: "Asymptotic Expansion of the Bergman Kernel for Steictly Pseudoconvex Complete Reinhardt Domains in C^2" Proc.Japan Acad.66. 39-41 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 板東 重稔: "Bubbling out of Einstein manifolds" Tohoku Math.J.42. 175-180 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 板東 重稔: "Removable singularities for holomorphic vector bundles" Tohoku Math.J.

    • Related Report
      1990 Annual Research Report
  • [Publications] 堀畑 和弘: "Pointwise property of L^pーfunctions with Nikolskii condition" Bolletino della Unione Matematica I taliana. 7. 199-207 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] Hitoshi ARAI: "Boundary behavior of functions on complete manifolds of negative curvature" Tohoku Mathematical Journal. 41. 307-319 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Hidekazu ITO: "Convergence of Birkhoff normal forms for integrable systems" Commentari Mathematici Helvetici. 64. 412-461 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Kazuhiro KONNO: "Generic Torelli theorem for hypersurfaces of certain homogeneous Kahler manifolds" Duke Mathematical Journal. 59. 83-160 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Takeyuki NAGASAWA: "Lp,q-estimates for semi-linear parabolic equations" Tohoku Mathematical Journal. 41. 597-608 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Kaoru ONO: "Equivariant index of Dirac operators" Tohoku Mathematical Journal. 42. (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] Kazuyuki SAITO: "Representation of C^*-algebra and regular completions" Journal of London Mathematical Society. 40. (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Hidekazu ITO: "Action-angle coordinates at singularities for analytic integrable systems" Mathematishe Zeitschrift.

    • Related Report
      1989 Annual Research Report
  • [Publications] Junji KATO: "Compact boundedness in periodic functional differential equations with infinite delay" Proceeding of the Royal Society of Edinburgh.

    • Related Report
      1989 Annual Research Report
  • [Publications] Junji KATO: "Stability via Liapunov functions with discontinuous derivatives" Journal of Mathematical Analysis and Applications.

    • Related Report
      1989 Annual Research Report
  • [Publications] Takeyuki NAGASAWA: "Asymptotical stability of Yang-Mill's gradient flow" Geometry of Manifolds(Academic Press). 499-517 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Kaoru ONO: "Periodic Schrodinger operator on a manifold" Forum Mathematicum. 1. 69-79 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Izumi TAKAGI: "On the shape of least-energy solutions to a semi-linear Neumann problem"

    • Related Report
      1989 Annual Research Report

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Published: 1989-04-01   Modified: 2016-04-21  

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