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Riemann-Hilbert problem

Research Project

Project/Area Number 09640229
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionKanagawa University

Principal Investigator

CHO Muneo  Kanagawa University, Faculty of Engineering, Professor, 工学部, 教授 (10091620)

Project Period (FY) 1997 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1999: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1998: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1997: ¥300,000 (Direct Cost: ¥300,000)
KeywordsRiemann-Hilbert problem / Hilbert space / Linear operator / Putnam inequality / p-hyponomal operator / Singular intergral model / Taylor spectrum / Xia spectrum / Riemann-Hilbert問題 / symbol / Weylの定理
Research Abstract

The title of my research is "Riemann-Hilbert problem"(No.09640229). I studied this problem from Heisei 9th to 11th. I made 16 manuscripts in this period, 9 manuscripts already pubrished and remaining 7 manuscripts are printing. I studied this problem the following steps :
(1) Making new spectral mapping theorems for p-hyponormal operators.
(2) Making new general polar symbols for p-hyponormal operators.
(3) Making new singular integral model for p-hyponormal operators.
(4) Extending Putnam inequality to n-tuples.
(5) Extending p-hyponormal operators to Riemann-Hilbert problem
Steps (1) - (3) are for the research of (4) and (5). I got almost final results of these steps. Hence I finished (5) in this research period. About (4), I got some information. I made two manuscripts of this problem. Professor Tadasi Huruya is very important. I got his help. Also, I asked to come to Japan to Professor W.Zelazko, he is a professor of the Banach Institute, in Heisei 10th. And in Heisei 11th I asked to come to Japan to Professor R.Curto, he is a professor of the University of Iowa. We discussed the problem (4) and got two munscripts.

Report

(4 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report
  • Research Products

    (36 results)

All Other

All Publications (36 results)

  • [Publications] 長宗雄,古谷正,伊藤益生: "Singular integral model for p-hyponormal operations and Rieman-Hilbert problem"Studia Math.. 130. 213-221 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 長宗雄,古谷正,伊藤益生: "Rieman-Hilbert problem for characteristic function of p-hyponormal operators"Acta Sci. Math. (Szeged). 64. 271-279 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 長宗雄,古谷正: "Putnam's inequality for p-hyponormal operators"Glasgow Math. J.. 41. 13-17 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 長宗雄: "Relations between the Taylor spectrum and Xia spectrum"Proc. Amer. Math. Soc.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 長宗雄,古谷正,伊藤益生: "Spectra of completely log-hyponormal operators"Integr. Equat. Oper. Th.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 長宗雄,B.Duggal,W.Y.Lee: "Putnam's inequality of log-hyponormal operators"Proc. Royal Irish Acad.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho and M.Itoh: "Weyl's Theorem holds for p-hyponormal operators"Glasgow Math. J.. 39. 217-220 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho, T.Huruya and M.Itoh: "Singular integral mode for p-hyponormal operators and the Riemann-Hilbert problem"Sudia Math.. 130. 213-221 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho, T.Huruya and M.Itoh: "Riemann-Hilbert problem for characteristic functions of p-hyponormal operators"Acta Sci. Math.(Szeged). 64. 271-279 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho and O.Nagano: "Spectral mapping theorems and Weyl spectra for hyponormal operators"Nihonkai Math. J.. 9. 105-110 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho, T.Huruya and B.Duggal: "Corrigendum to "On the spectrum of p-hyponormal operators""Acta Sci. Math. (Szeged). 64. 739-740 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho and O.Nagano: "Simple proof of the p-hyponormality of the Aluthge transformations"Integr. Equat. Oper. Th.. 33. 248-251 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho, T.Huruya: "Putnam's inequality for p-hyponormal n-tuples"Glasgow Math. J.. 41. 13-17 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho and B.Duggal: "p-hyponormal operactors-functional transformations and spectra"SCM. 2. 141-144 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho and K.Tanahashi: "Spectral properties of log-hyponormal operators"SCM. 2. 223-230 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho: "Relations between the Taylor spectrum and the Xia spectrum"Proc. Amer. Math. Soc.. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho, T.Huruya and M.Itoh: "Spectra of completely log-hyponormal operators"Integr. Equat. Oper. Th.. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho, I.H.Jeon and J.I.Lee: "Joint spectra of doubly commuting n-tuples of operators and their Aluthge transforms"Nihokai Math. J.. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho, B.Duggal and W.Y.Lee: "Putnam's inequality of log-hyponormal operators"Proc. Roy. Irish Acad.. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho, I..H.Jeon and J.I.Lee: "Spectral and structural properties of log-hyponormal operators"Glasgow Math. J.. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho, I.H.Jeon, I.B.Jung, J.I.Lee and K.Tanahashi: "Joint spectra of n-tuples of operators of generalized Aluthge transformation"Rev. Roum. Math. Pures Appl.. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Cho, T.Huruya and Y.O.Kim: "A note on w-hyponormal operators"J. Inequal. Appl.. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 長宗雄,古谷正,伊藤益生: "Riemann-Hilbertproblem for characteristic functions of p-hyponoromal operators"Acta Sci. Math. (Szeged). 64. 271-279 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 長宗雄,古谷正,B.P.Duggal: "Corrigendum to "On the spctrum of p-hyponormal operators"."Acta Sci. Math. (Szeged). 64. 739-740 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 長宗雄,永野興彦: "Simple proof of p-hyponormality of the Aluthge Trnsformations"Integr. Equat. Oper Th.. 33. 248 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 長宗雄,古谷正: "Putnam's inequality for p-hyponormal n-tuples"Glasgow Math.J.. 41. 13-17 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 長宗雄,棚橋浩太郎: "Spectral properties of log-hyponormal operators"SCM. 2. 223-230 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 長宗雄: "Relations between the Taylor spectrum and the Xia spectrum"Proc. Amer. Math. Soc..

    • Related Report
      1999 Annual Research Report
  • [Publications] 長 宗雄、古谷 正、伊藤益生: "Singular integral models for p-hyponormal operatorsand Riemann-Hilbert problem" Studia Math.130. 213-221 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 長 宗雄、古谷 正、伊藤益生: "Rimann-Hilbert problem for characteristic functions of p-hyponomal operators" Acta Sci.Math.(Szeged). 64. 271-279 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 長 宗雄、永野興彦: "Spectral mapping theorems and Weyl spectra for hyponormal operators." Nihonkai Math.J.9. 105-110 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 長 宗雄、古谷 正、B.P.Duggal: "Corrigendum to “On the spectrum of p-hyponormal operators"" Acta Sci.Math.(Szeged). 64. 739-740 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 長宗雄, 伊藤益生, 大城覚: "Weyl's theorem holds for p-hyponormal operators." Glasgow Math.J.39. 217-220 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 長宗雄, 伊藤益生: "Fuzzy bounded operators" Fuzzy sets and systems. 93. 353-362 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 長宗雄, 古谷正: "Putnam's inequality for p-hyponormal n-tuples" Glasgow Math.J.

    • Related Report
      1997 Annual Research Report
  • [Publications] 長宗雄, 古谷正, 伊藤益生: "Singular integral models for p-hyponormal operators and Riemann-Hilbert problem" Studia Math.

    • Related Report
      1997 Annual Research Report

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

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