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Fourier Analysis and Order Structure

Research Project

Project/Area Number 09640215
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionHokkaido Institute of Technology

Principal Investigator

KOSHI Shozo  Hokkaido Inst.Tech., Gen.Edu., Professor, 教養部, 教授 (40032792)

Co-Investigator(Kenkyū-buntansha) KANETA Takashi  Hokkaido Inst.Tech., Gen.Edu., Prof., 教養部, 教授 (50145984)
WAJIMA Masayuki  Hokkaido Inst.Tech., Gen.Edu., Prof., 教養部, 教授 (20201163)
KIMURA Nobuyuki  Hokkaido Inst.Tech., Gen.Edu., Prof., 教養部, 教授 (10204984)
TAKAHASHI Yuji  Hokkaido Univ.of Edu., Prof., 函館校, 教授 (00179540)
YAMAGUCHI Hiroshi  Josai Uni., Dept.Science, Prof., 理学部, 教授 (20137798)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1997: ¥1,700,000 (Direct Cost: ¥1,700,000)
Keywordshypergroup / F.and M.Riesz theorem / Riesz-Fisher's theorem / ordered topological linear space / generalized supremum / weak Fatou property / Harmonic analysis on group / Riesz space / F.and M.Ries2 theorem / Rise2 space / ordered topological opaco / Ries2-Fisher's theorem / harmanic analysis on group / convex cone / disk hypergroup / F.and M.Riess theorem / ordered linear spaco / topological ordered space / parmonic analysis on group
Research Abstract

1. Study on Fourier Analysis
(a) We can extend the F.and M.Riesz theorem in the case of hypergroup and non-Abelian compact group. Before, these considerations are made in only Abelian cases.
(b) Bochner's theorem says that product of two Riesz sets is also a Riesz set. In the case of loyally compact Abelian group, Bochner's thearem is true by H.Yamaguchi. This time, we can prove that Bochner's theorem is valid in non-Abelian compact group.
(c) Fourier Analysis in Disk hypergroup can be developed by many peoples. We can extend these theory in the case of discrete hyper group.
2. Study on Order Structure.
(a) Normed linear space with Fatou property is complete (Riesz-Fisher's theorem) is not true in general ordered topological inear space. We find a necessary and sufficient condition tWat the Riesz-Fisher's theorem is valid in the space.
(b) We defined generalized suprernum ( or generalized infimum) for a order bounded sub set. We investigate properties of generalized suprem ( or generalized infimum). We construct a theory of generalized supremum and generalized infimum. We find that distributive law is valid if and only if the space is a Riesz space.
(c) Optimization theory usually considers only real valued functions. We construct an optimization theory for function whose value is taken in an ordered topological linear space. For application, this theory is very important.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (29 results)

All Other

All Publications (29 results)

  • [Publications] S.Koshi: "A generalization of the Amemiya′s theorem" proceedings of Prague Mathematical conference. 1996. 135-140 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Koshi: "Lattice structure of partially ordered linear space" Memoir of the Hokkaido Institute of Technology. 25. 9-15 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Koshi, S.Dimiev & R.Lazov: "Partially ordered normed linear space with weak Fatou pro-perty" Taiwanese Journal of Mathematics. 1. 1-9 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Koshi: "Order operation in partially ordered linear space" Memoir of the Hokkaido Institute of Technology. 26. 263-270 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Koshi: "Distributive law in partially ordered linear space" Symposium on Real Analysis. 181-188 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Yamaguchi: "On the product of Riesz sets in dual objects of compact groups" Reports on Function space seminar. 89-91 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Heyer & S.Koshi: "Harmonic Analysis on the Disk Hypergroup (2ed edition)" Mathematical Seminar Note, Tokyo Metropolitan University, 94 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Koshi: "A generalization of the Amemiya's theorem" Proceeding of Prague Mathematical conference. 135-140 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Koshi: "Lattice structure of partially ordered linear space" Memoir of the Hokkaido Institute of Tech.25. 9-15 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Koshi: "Dimiev & R.Lazov : Partially ordered normed linear space with weak Fatou property" Taiwanese Journal of Mathematics. 1. 1-9 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Koshi: "Order operation in partially ordered linear space" Memoir of the Hokkaido Institute of Tech.26. 262-270 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Koshi: "Distributive law in partially ordered linear space" Symposium on Real Analysis, Kagawa University. 181-188 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Yamaguchi: "On the product of Riesz sets in dual objects of compact grouops" Reports on Function space seminar, Hokkaido University. 89-91 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Heyer &S.Koshi: Harmonic Analysis on the Disk Hypergroup (2ed edition). Mathematical Seminer Note Tokyo Metropolitan University, 94 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Koshi: "A generalization of the Amemiya's theorem" Proceedings of Praque Mathematical conference. 135-140 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Koshi & N.Komuro: "Supsets on partially ordered topological linear space" Taiwanese Journal of Mathematics. accepted printed. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Koshi: "Distributive law in partially ordered linear space" Symposium on Real Analysis. 181-188 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Koshi & N.Komuro: "Ordered topological linear space" Reports on Function space seminar. 116-119 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Yamaguchi: "On the product of Riesz sets in dual objects of compact groups" Reports on Functino space seminar. 89-91 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] N.Kimura & others: "Molecular dynamics theory of complex magnetic structure in itinerant magnets" J.of Magnetism and Magnetic Materials. 177-181. 573-574 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Heyer & S.Koshi: "Harmonic Analysis on the Disk Hypergroup" Mathematical Seminar Notes,Tokyo Metropolitan University, 94 (1996)

    • Related Report
      1998 Annual Research Report
  • [Publications] Shozo Koshi: "Lattice structure of partially ordered linear space" Memoir of the Hokkaido Institute of Technolohy. 25. 9-15 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Koshi,S.Dimiev,R.Lazov: "Partially ordered normed linear space with weak Fatou property" Taiwanese Journal of Mathematics. 1-1. 1-9 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Shozo Koshi: "Order operation in partially ordered linear space" Memoir of the Hokkaido Institute of Technology. 26. 263-270 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hiroshi Yamaguchi: "The space N (σ) and the F.and M.Riesz theorem" Hokkaido Mathematical Journal. 15-3. 567-589 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] Yuji Takahashi: "Some counterexamples in amenability" Transactions of Tubingen University. 216-223 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Kimura and others: "Morecular dynamics approach to Itinerant magnetism with complex magnetic structure" Phisica.B. 502. 237-238 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Editor J.Lawrynowicz: "Deformation of Mathematical Structure S.Koshi" Kluwer Academic Publisher, 500(216-283) (1993)

    • Related Report
      1997 Annual Research Report
  • [Publications] Banach Center (editor): "S.Koshi Recent developements on the F.and M.Riesz theorem" Polish Academy of Sciences, 400 (1995)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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