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Studies of Harmonic Analysis

Research Project

Project/Area Number 60460003
Research Category

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

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionTOHOKU UNIVERSITY

Principal Investigator

IGARI Satoru  Faculty of Sciences, To"hoku University Professor, 理学部, 教授 (50004289)

Co-Investigator(Kenkyū-buntansha) SATO Shuichi  Faculty of Sciences, To"hoku University Assistant, 理学部, 助手 (20162430)
OKADA Masami  Faculty of Sciences, To"hoku University Lecturer, 理学部, 講師 (00152314)
HOTTA Tyoshi  Faculty of Sciences, To"hoku University Professor, 理学部, 教授 (70028190)
KATO Junji  Faculty of Sciences, To"hoku University Professor, 理学部, 教授 (80004290)
MASUDA Kyuya  Faculty of Sciences, To"hoku University Professor, 理学部, 教授 (10090523)
Project Period (FY) 1985 – 1986
Project Status Completed (Fiscal Year 1986)
Budget Amount *help
¥6,500,000 (Direct Cost: ¥6,500,000)
Fiscal Year 1986: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 1985: ¥3,300,000 (Direct Cost: ¥3,300,000)
KeywordsHarmonic function / subharmonic function / Hardy space / Operator algebra / Evolution equation / Semi-simple group / D-module / 補間定理
Research Abstract

Classical harmonic analysis has been a considerable flowering duaring the past 15 years starting from the results due to Fefferman-Stein,Carleson and others. The object of our program was to study the idea of classical harmonic analysis and to develop it in various fields in mathematics by the coorperative research with several specialists in our institute.An extract of our results is the following :
1. An interpolation theorem of operators on a product measure space is shown. As applications we solved partially a problem on Riesz-Bochner means and on Kakeya's maximal function. Hardy spaces on a product space are investigated with connection to holomorphic functions of two variables.We are now generalizing classical Hardy space theory to a manifold of negative curvature.
2. We have studied non-linear evolution equations getting several results on a property of the solutions of Navier-Stokes equation near t = 0, existence of global solutions and analiticity of solutions.
3. By a method of D-modules it is succeeded to analyse and classify the singularities of characters through Harish-Chandra's differential equation. We have a program to develop these researches in future.

Report

(1 results)
  • 1986 Final Research Report Summary
  • Research Products

    (13 results)

All Other

All Publications (13 results)

  • [Publications] IGARI Satoru: Tohoku Math.J.38. 469-490 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] MASUDA,Kyuya;Kato,T.: Ann.Inst.Henri Poincare. 3. 455-467 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] HOTTA Ryoshi: Advances Studies in Pure Math.6. 127-138 (1985)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] KATO,Junji: J.Diff.Eq.65. 269-286 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] OKADA,Masami;Gaveau,B.;Okada,T.: C.R.Acad.Sc.,Paris. 302. 21-24 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] SATO,Shuichi: Trans.Amer.Math.Soc.39. 35-53 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] HOTTA,Ryoshi: "Introduction to D-Modules" Institute of Mathematical Sciences,Madras, (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] IGARI,Satoru: "Interpolation of linear operators in Lebesgue spaces with mixed norm and its applications to Fourier analysis" Tohoku Mathematical Journal. 38. 469-490 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] MASUDA Kyuya; KATO,Toshio: "Non-linear evolution equation and analyticity" Annales Institut Henri Poincare. 3. 455-467 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] HOTTA, Ryoshi: "Local formula for Springer's representation" Advanced Studies in Pure Mathematics. 6. 127-138 (1985)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] KATO, Junji: "On a boundedness condition for solutions of a generalized Lienard equation" Journal of Differential Equations. 65. 269-286 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] OKADA, Masami; Gaveau,B; Okada,T: "Operateurs du second order coefficients irreguliers en une dimension et leur calcule fonctionnel" C.R.Acad Sc.,Paris. 302. 21-24 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] HOTTA, Ryoshi: Institute of Mathematical Sciences, Madras. Introduction to D-Modules, (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary

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Published: 1987-03-31   Modified: 2016-04-21  

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