• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Functional analysis and applications

Research Project

Project/Area Number 08304011
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section総合
Research Field 解析学
Research InstitutionHIROSHIMA UNIVERSITY

Principal Investigator

OHARU Shinnosuke  Hiroshima-U., Mathematics, Professor, 理学部, 教授 (40063721)

Co-Investigator(Kenkyū-buntansha) TAKENAKA Sigeo  Okayama Scinece U., Mathemathics, Professor, 理学部, 教授 (80022680)
YABUTA Kozo  Nara womans U., Mathematics, Professor, 理学部, 教授 (30004435)
NAKAZI Takahiko  Hokkaido U., Mathematics, Professor, 理学部, 教授 (30002174)
OHYA Masanori  Tokyo Science U., Mathematics, Professor, 理工学部, 教授 (90112896)
KOMATSU Hikosaburo  Tokyo Science U., Mathematics, Professor, 理学部, 教授 (40011473)
Project Period (FY) 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥5,000,000 (Direct Cost: ¥5,000,000)
Fiscal Year 1996: ¥5,000,000 (Direct Cost: ¥5,000,000)
KeywordsHardy space / Toeplitz operator / Littlewood-Paley operator / evolution operator / nonlinear evolution problem / pseudo-differential operator / information dynamics / stable stochastic field / 不変部分空間 / 非線形解析
Research Abstract

Functional analysis is a diverse field and a great number of results on a variety of mathematical problems arising in the current mathematical sciences have been produced. In this research project it was aimed at making a significant contribution to the studies in functional analysis and its applications. The emphasis was layd on was function algebra, operator theory, theoretical development of nonlinear analysis, detailed freatments of mathematical models involving differential equations, generalized functions with applications to physics, and information theory based on operator algebra.
1.Inportand results on outer functions, weighted Hardy spaces, Toeplitz operators and invariant subspaces were obtained and Littlewood-Paley operators were investigated in new aspects.
2.In consideration of nonlinear problems arising in various mathematical models, an extensive study of evolution operators as well as its applications to those problems was made with the aid of the newest results on infi … More nite dimensional dynamical systems, pde's and numerical analysis.
3.Generalized functions were treated in terms of pseudo-differential operator theory, Toeplitz operator and generalized solutions of differential equations.
4.By means of new methods invented in functional analysis and stochastic calculus, theory of information dynamics was advanced. Extensive studies of various problems on boundary domains were made interms of complexity.
5.New results on determinism in stable stochastic fields were obtained and infinitely decomposable processes were investigated in various aspects.
A great deal of progress has been constantly made in functiona analysis and its applications. In order to pursue such studies, effective research collaboration with specialists in the related fields is particularly important. Owing to the grant-in-aid, most of the aimed results were obtained. In particular, an international conference on evolution equations and their applications to technolog was held with the participation of leading scientists in those fields and this support is greatly appreciated. Less

Report

(2 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • Research Products

    (18 results)

All Other

All Publications (18 results)

  • [Publications] 大春愼之助: "Nonlinear perturbations of a class of integrated semigroups" Hiroshima Math.J.26・3. 433-473 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 小松彦三郎: "Laplace 超函数による微分方程式の解法,超函数と微分方程式" 数理解析研究所講究録. 935. 21-52 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 大矢雅則: "Note on quantum dynamical entropies" Rep.Math.Phys.38・3. 457-46 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 中路貴彦: "An outer function and severalimportant in two variables" Arch.Math.173. 219-226 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 中路貴彦: "Riesz's functions in weighted Hardy and Bergman spaces" Canad.J.Math.48. 930-945 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 薮田公三: "Littlewood-Paley operators on the generalized Lipschitz spaces" Georgian Math.J.3. 69-80 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Shinnosuke Oharu, T.Matsumoto and H.R.Thieme: "Nonlinear perturbations of a class of integrated semigroups" Hiroshima Math.J.26(3). 433-473 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Hikosaburo Komatsu: "Solution of differential equations by means of Laplace hyperfunctions" World Scientific, Structure of Solutions of Differential Equations. 227-252 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Masanori Ohya, L.Accardi and N.Watanabe: "Note on quantum dynamical entropies" Rep.Math.Phys.Vol.38, No.3. 457-469 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Takahiko Nakazi: "An outer fnction and severalimportant in two variables" Arch.Math.173. 219-226 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Takahiko Nakazi and M.Yamada: "Riesz's functions in weighted Hardy and Bergman spaces" Canad.J.Math.48. 930-945 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Kouzou Yabuta, Shanzhen Lu and Changmei Tan: "Littlewood-Paley operators on the generalized Lipschitz spaces" Georgian Math.J.3. 69-80 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 大春愼之助: "Nonlinear perturbations of a class of integrated semigroups" Hiroshima Math. J.26・3. 433-473 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 小松彦三郎: "Laplace超函数による微分方程式の解法,超函数と微分方程式" 数理解析研究所講究録. 935. 21-52 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 大矢 雅則: "Note on quantum dynamical entropies" Rep. Math.Phys.38・3. 457-469 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 中路 貴彦: "An outer function and severalimportant in two variables" Arch. Math.173. 219-226 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 中路 貴彦: "Riesz's functions in weighted Hardy and Bergman spaces" Canad. J. Math.48. 930-945 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 薮田 公三: "Littlewood-Paley operators on the generalized Lipschitz spaces" Georgian Math. J.3. 69-80 (1996)

    • Related Report
      1996 Annual Research Report

URL: 

Published: 1996-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi