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STUDIES ON FUNCTIONAL AND REAL ANALYSES VIA UNIVERSAL AND UNIFIED APPROACH

Research Project

Project/Area Number 03302004
Research Category

Grant-in-Aid for Co-operative Research (A)

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

Principal Investigator

OKAYASU Takateru  Faculty of Science,Yamagata University,Professor, 理学部, 教授 (60005775)

Co-Investigator(Kenkyū-buntansha) NISHISHIRAHO Toshihiko  Faculty of Science,Ryukyu University,Professor, 理学部, 教授 (70044956)
KOMASTU Hikosaburo  Department of Mathematical Sciences,The University of Tokyo,Professor, 大学院・数理科学研究科, 教授 (40011473)
HUJIWARA Hidenori  Faculty of Engineering in Kyushu,Kinki University,Professor, 九州工学部, 教授 (50108643)
OHYA Masanori  Faculty of Science and Technology,Science University of Tokyo,Professor, 理工学部, 教授 (90112896)
SAITO Kichisuke  Faculty of Science,Niigata University,Professor, 理学部, 教授 (30018949)
伊藤 清三  杏林大学, 社会科学部, 教授 (40011423)
三鳥川 寿一  津田塾大学, 学芸学部, 教授 (80055318)
井上 淳  福岡大学, 理学部, 教授 (50078557)
Project Period (FY) 1991 – 1992
Project Status Completed (Fiscal Year 1992)
Budget Amount *help
¥16,800,000 (Direct Cost: ¥16,800,000)
Fiscal Year 1992: ¥9,400,000 (Direct Cost: ¥9,400,000)
Fiscal Year 1991: ¥7,400,000 (Direct Cost: ¥7,400,000)
KeywordsJones index / Completely positive maps / Entropies of quantum systems / Quantum groups / Infinite-dimensional Lie groups and Lie algebras / Evolution equation / Schrodinger operators / Microlocal analysis / Jones index / 非有界作用素環 / 情報力学 / 非線形関数解析 / 拡散方程式 / 幾何学的方程式 / 対称空間上の調和解析 / 佐藤超関数
Research Abstract

Details of results (including names of contributors) should be found in "THE RESEARCH REPORT"; We will state only the research objects with which each research group has mainly concerned through the project.
(1)(Research group on operator algebras and function algebras) Index theory for II_1 factors, completely positive maps, non-abelian dynamical systems, Kac groups and quantum groups (Operator algebra theory), and Douglas algebras, Bourgain algebras, Toeplitz and Hankel operators, etc. (Function algebra theory), are investigated in this group; many results which seem to be important arer given.
(2)(Research group on Banach function spaces) Non-commutative processes (stability of their system), Clarkson type inequality, (linear, semi-linear, and non-linear) evolution equation, entropies of quantum systems (with applications to heredity theory), non-linear Perron-Frobenius theory, outer functions, etc., are investigated from various stand points and many results are obtained.
(3)(Research … More group on representation theory) Representations of quantum groups, infinite-dimensional Lie groups, and Lie algebras and their representations, Kostant theory and Feynman path integral, homogeneous spaces of semi-simple Lie groups, etc., were investigated extensively.
(4)(Research group on partial differential equations) Semigroups of operators and evolution equation, asymptotic behavior of interfaces and blow-up of solutions for non-linear equations, Scattering theory for Schrodinger operators, mathematical study of quantum field theory, WKB method,microlocal analysis, Torotter type formulas, etc., were studied and added greately to our knowledge of the theory.
(5)(Research group on real analysis) Studies on global density theorem for Federer measures, Sato's generalized functions valued in locally convex spaces, Fefferman-Phong inequality, quasi-invariant measures for commutative transformation groups, extrapotation for infinite measure spaces, etc., are aimed and results which seem to be influential are obtained. Less

Report

(3 results)
  • 1992 Annual Research Report   Final Research Report Summary
  • 1991 Annual Research Report

Research Products

(28 results)

All Other

All Publications (28 results)

  • [Publications] T.Okayasu: "The von Neumann inequality and dilation theorems for contractions" Operator Theory:Advances and Applications. 59. 285-291 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] K.-S.Saito: "A simple approach to the invariant subspace structure of analytic crossed products" To appear in Jornal of Operator Theory.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] M.Ohya and N.Muraki: "Note on continuity of information ratio" Illenois Journal of Math.36. 529-550 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H.Hujiwara: "Sur les restrictions des representations unitaires des groupes de Lie resolubles exponentiels" Invent.Math.104. 647-654 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H.Komastu: "Microlocal analysis in Gevrey classes and in complex domains in ¨Microlocal Analysis and Applications¨" Lecture Notes in Math.1495. 161-236 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.Nishishiraho: "The degree of the best approximation in Banach spaces" To appear in Tohoku Math.Journal.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] S.Ito: "Diffusion Equations" American Math Soc., 270 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H.Hujiwara: "Sur les restrictions des representations unitaires des groupes de Lie resolubles exponentiels." Invent.Math. 104. 647-654 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] S.Ito: "Diffusion Equations" American Math.Soc. (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] H.Komastu: "Microlocal analysis in Gevrey classes and in complex domains in "Microlocal Analysis and Applications"." Lecture Notes in Math. 1495. 161-236 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.Nishishiraho: "The degree of the best approximation in Banach spaces" Tohoku Math.Journal.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] M.Ohya and N.Muraki: "Note on continuity of information ratio" Illinois Journal of Math. 36. 529-550 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.Okayasu: "The von Neumann inequality and dilation theorems for contractions, Operator Theory" Advances and Applications. 59. 285-291 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] K.-S.Saito: "A simple approach to the invariant subspace structure of analytic crossed products" in Journal of Operator Theory.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] T.Okayasu: "The von Neumann inequality and dilation theorems for contractions" Operator Theory:Advances and Applications. 59. 285-291 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] k.-S.Saito: "A simple approach to the invariant subspace structure of analytic crossed products" To appear in Jornal of Operator Theory.

    • Related Report
      1992 Annual Research Report
  • [Publications] M.Ohya and N.Muraki: "Note on continuity of information ratio" Illinois Journal of Math.36. 529-550 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] H.Hujiwara: "Sur les restrictions des representations unitaires des groupes de Lie resolubles exponentiels" Invent.math.104. 647-654 (1991)

    • Related Report
      1992 Annual Research Report
  • [Publications] H.Komastu: "Microlocal analysis in Gevrey classes and in complex domains in¨Microlocal Analysis and Applications¨" Lecture Notes in Math.1495. 161-236 (1991)

    • Related Report
      1992 Annual Research Report
  • [Publications] T.Nishishiraho: "The degree of the best approximation in Banach spaces" To appear in Tohoku Math.Journal.

    • Related Report
      1992 Annual Research Report
  • [Publications] S.Ito: "Diffusion Equations" American Math.Soc., 270 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] T.Okayasu: "The von Neumann inequality and dilation theorems for contractions" To appear in Proc.Workshop on Oprator Theory and Complex Analysis (Hokkaido,1991).

    • Related Report
      1991 Annual Research Report
  • [Publications] J.ーP.Antoine and A.Inoue: "Partial*ーalgebras of closed operator II.States and representations of partial *ーalgebras" Publ.RIMS,Kyoto Univ.27. 399-430 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.Ohya: "Information dynamics and its application to optical communication processes" Springer Lecture Notes in Physics. 378. 81-92 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] S.Oharu: "Non Iinear perturbations of analytic semigrops" Semigroup Forum. 42. 127-146 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Giga: "Motion of hypersurfaces and geometric equations" Journ.Math.Soc.Japan. 44. 99-111 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] T.Nishishiraho: "Convergence of positive Iinear operators" AttiSem.Mat.Fis.Univ.Modena. 29. 367-374 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] S.Ito: "American Math.Soc." Diffusion Equations, 270 (1992)

    • Related Report
      1991 Annual Research Report

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Published: 1991-03-31   Modified: 2016-04-21  

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