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Study of integral transformations in hyperfunctions and differential operators of infinite order

Research Project

Project/Area Number 22540173
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionChiba University

Principal Investigator

OKADA Yasunori  千葉大学, 理学(系)研究科(研究院), 教授 (60224028)

Co-Investigator(Renkei-kenkyūsha) ISHIMURA Ryuichi  千葉大学, 大学院理学研究科, 教授 (10127970)
Research Collaborator LIESS Otto  ボローニャ大学, 教授
Project Period (FY) 2010-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords超函数 / 無限階微分作用素 / 擬微分作用素
Outline of Final Research Achievements

On kernel theorems in hyperfunctions, we got some partial results for the purpose of the study on locally convex cases. We established the division by differential operators of infinite order with parameters and its variant related to BMT classes, and got the support properties and the analytic singular support properties for integral transformations. We also worked on bounded hyperfunctions at infinity, and gave a notion of fading memory for operators with infinite delay. Moreover we got results on boundary value representations, dualities, and periodic equations.

Report

(6 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (20 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (6 results) (of which Peer Reviewed: 4 results) Presentation (14 results)

  • [Journal Article] Ultra-differentiable classes and intersection theorems2014

    • Author(s)
      Otto Liess and Yasunori Okada
    • Journal Title

      Mathematische Nachrichten

      Volume: 287

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Massera type theorems in hyperfunctions with reflexive Banach values2013

    • Author(s)
      Yasunori Okada
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B40

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Boundary value representations for bounded hyperfunctions and some variants2013

    • Author(s)
      Yasunori Okada
    • Journal Title

      数理解析研究所講究録

      Volume: 1861

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Support properties for integral operators in hyperfunctions2012

    • Author(s)
      Otto Liess and Yasunori Okada
    • Journal Title

      Advances in Mathematics

      Volume: 231 Issue: 3-4 Pages: 1439-1461

    • DOI

      10.1016/j.aim.2012.07.002

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A notion of boundedness for hyperfunctions and Massera type theorems2012

    • Author(s)
      Yasunori Okada
    • Journal Title

      Banach Center Publications

      Volume: 97 Pages: 101-111

    • DOI

      10.4064/bc97-0-7

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 有界超函数と周期線形函数方程式について2011

    • Author(s)
      岡田靖則
    • Journal Title

      数理解析研究所講究録

      Volume: 1723 Pages: 179-190

    • Related Report
      2010 Annual Research Report
  • [Presentation] Solvability of coupling equations and infinite dimensional holomorphy2014

    • Author(s)
      Yasunori Okada
    • Organizer
      Several aspects of microlocal analysis
    • Place of Presentation
      京大数理研, 京都
    • Year and Date
      2014-10-21
    • Related Report
      2014 Annual Research Report
  • [Presentation] Bounded hyperfunctions and Massera type theorems2014

    • Author(s)
      Yasunori Okada
    • Organizer
      International Conference on Generalized Functions
    • Place of Presentation
      Southampton, UK
    • Year and Date
      2014-09-09
    • Related Report
      2014 Annual Research Report
  • [Presentation] Coupling equations and infinite dimensional holomorphy2014

    • Author(s)
      Yasunori Okada
    • Organizer
      Formal and analytic solutions of functional equations
    • Place of Presentation
      Valladolid, Spain
    • Year and Date
      2014-09-03
    • Related Report
      2014 Annual Research Report
  • [Presentation] Bounded hyperfunctions and Massera type theorems2013

    • Author(s)
      Yasunori Okada
    • Organizer
      偏微分方程式姫路研究集会
    • Place of Presentation
      姫路モノリス, 姫路
    • Related Report
      2012 Annual Research Report
  • [Presentation] A functional approach to bounded hyperfunctions2013

    • Author(s)
      Yasunori Okada
    • Organizer
      Recent development of theory of analytic functionals and related topics
    • Place of Presentation
      北大, 札幌
    • Related Report
      2012 Annual Research Report
  • [Presentation] Boundary value representations for bounded hyperfunctions and some variants2012

    • Author(s)
      Yasunori Okada
    • Organizer
      Recent development of microlocal analysis and asymptotic analysis
    • Place of Presentation
      RIMS, 京都
    • Related Report
      2012 Annual Research Report
  • [Presentation] Massera type theorems in hyperfunctions with reflexive Banach values2011

    • Author(s)
      岡田靖則
    • Organizer
      漸近解析に於ける超局所解析の展望
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-11-15
    • Related Report
      2011 Annual Research Report
  • [Presentation] A notion of boundedness for hyperfunctions and Massera type theorems2011

    • Author(s)
      岡田靖則
    • Organizer
      FASDE II
    • Place of Presentation
      ベドレボ数学研究所,Poland
    • Year and Date
      2011-08-11
    • Related Report
      2011 Annual Research Report
  • [Presentation] Massera type theorems for linear functional equations with infinite delay in hyperfunctions2011

    • Author(s)
      岡田靖則
    • Organizer
      Equadiff 2011
    • Place of Presentation
      ラフバラ大学,UK
    • Year and Date
      2011-08-05
    • Related Report
      2011 Annual Research Report
  • [Presentation] Massera type theorems in hyper舳nctions2010

    • Author(s)
      岡田靖則
    • Organizer
      研究集会NEW DIRECTIONS IN ANALYSIS
    • Place of Presentation
      ベトナム理工学アカデミー数学研究所(ベトナム)
    • Year and Date
      2010-08-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Massera type theorems in hyperfunctions with values in a reflexive locally convex space

    • Author(s)
      Yasunori Okada
    • Organizer
      The Asian Mathematical Conference 2013
    • Place of Presentation
      BEXCO, Busan, Korea
    • Related Report
      2013 Annual Research Report
  • [Presentation] Massera type theorems in vector-valued analytic functions and hyperfunctions

    • Author(s)
      Yasunori Okada
    • Organizer
      Formal and Analytic Solutions of Differential, Difference and Discrete Equations
    • Place of Presentation
      Bedlewo, Poland
    • Related Report
      2013 Annual Research Report
  • [Presentation] 非古典的な第2超関数の例とフーリエ逆変換

    • Author(s)
      Yasunori Okada
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      東京大学玉原国際セミナーハウス, 玉原
    • Related Report
      2013 Annual Research Report
  • [Presentation] Coupling方程式における無限変数正則関数について

    • Author(s)
      Yasunori Okada
    • Organizer
      代数解析学と局所凸空間
    • Place of Presentation
      日大, 御茶ノ水
    • Related Report
      2013 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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