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The characterization of the closed range operator and the invariant subspace using the sampling set

Research Project

Project/Area Number 20740070
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionOtaru University of Commerce

Principal Investigator

YONED Rikio  Otaru University of Commerce, 商学部, 准教授 (70342475)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsベルグマン空間 / ハーディー空間 / 荷重付きディクレ空間 / 閉値域 / 掛け算作用素 / サンプリング集合 / テープリッツ作用素 / 積分作用素 / ハンケル作用素 / 不変部分空間 / ディリクレ空間 / 合成作用素 / 補間点列
Research Abstract

I researched the operators on the weighted Dirichlet spaces. In particular, I studied the multiplication operator and the Toeplitz operator and the Hankel operator on the weighted Dirichlet space with the closed range. It is well-known with respect to the closed range multiplication operator, but there is no result with respect to the closed range Toeplitz operator and Hankel operator on the weighted Dirichlet space. So I studied the sampling set with respect to the analytic symbol multiplication operator. Moreover I get the results when Toeplitz operator and Hankel operator have the closed range on the weighted Dirichlet spaces.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (16 results)

All 2010 2009 2008 Other

All Journal Article (2 results) Presentation (14 results)

  • [Journal Article] The characterization of the sampling set for Bloch-type spaces2008

    • Author(s)
      米田力生
    • Journal Title

      数理解析研究所講究録 1596

      Pages: 51-62

    • Related Report
      2008 Annual Research Report
  • [Journal Article] The characterization of the sampling set for Bloch-type spaces

    • Author(s)
      米田力生
    • Journal Title

      数理解析研究考究録 1596

      Pages: 51-61

    • Related Report
      2010 Final Research Report
  • [Presentation] 閉値域を持つハンケル作用素に関して2010

    • Author(s)
      米田力生
    • Organizer
      等角写像論・値分布論
    • Place of Presentation
      コラッセふくしま 小会議室403号
    • Year and Date
      2010-12-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] Hankel operators with closed range2010

    • Author(s)
      米田力生
    • Organizer
      解析セミナー
    • Place of Presentation
      北海道大学
    • Year and Date
      2010-11-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] The lower norm of the multiplication operators2009

    • Author(s)
      米田力生
    • Organizer
      第18回関数空間セミナー
    • Place of Presentation
      北海道大学
    • Year and Date
      2009-12-23
    • Related Report
      2009 Annual Research Report
  • [Presentation] The multiplication operator on the weighted Dirichret spaces2009

    • Author(s)
      米田力生
    • Organizer
      解析セミナー
    • Place of Presentation
      北海道大学
    • Year and Date
      2009-10-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] Interpo1ation sequence and closed range integration operators2008

    • Author(s)
      米田力生
    • Organizer
      第17回関数空間セミナー
    • Place of Presentation
      東京理科大学
    • Year and Date
      2008-12-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] カールソンの定理の拡張2008

    • Author(s)
      米田力生
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] The composition operator with closed range on the weighted Bloch space and the weighted Drichlet spaces

    • Related Report
      2010 Final Research Report
  • [Presentation] Composition operators on the weighted Dirichlet spaces with closed range

    • Related Report
      2010 Final Research Report
  • [Presentation] The characterizarion of the sampling set for Bloch-type spaces

    • Related Report
      2010 Final Research Report
  • [Presentation] Interpolation sequence and closed range integration operator

    • Related Report
      2010 Final Research Report
  • [Presentation] The multiplication operators on the weighted Dirichlet spaces

    • Related Report
      2010 Final Research Report
  • [Presentation] The lower norm of the multiplication operators

    • Related Report
      2010 Final Research Report
  • [Presentation] Hankel operator with closed range

    • Related Report
      2010 Final Research Report
  • [Presentation] 閉値域をもつハンケル作用素に関して

    • Related Report
      2010 Final Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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