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2016 Fiscal Year Research-status Report

等式の枠組による零形式の時空大域的研究

Research Project

Project/Area Number 16K13771
Research InstitutionWaseda University

Principal Investigator

小澤 徹  早稲田大学, 理工学術院, 教授 (70204196)

Co-Investigator(Kenkyū-buntansha) 田中 和永  早稲田大学, 理工学術院, 教授 (20188288)
BEZ NEAL  埼玉大学, 学内共同利用施設等, 准教授 (30729843)
Project Period (FY) 2016-04-01 – 2019-03-31
Keywords関数方程式 / 調和解析 / 実解析 / 変分解析
Outline of Annual Research Achievements

波動方程式に関する双線型作用素や運動論的輸送方程式に関する線型作用素の有界性について、新しい評価を証明することができ深い理解が得られた。また、加藤・ポンセ型の交換作用素や分数冪ライプニッツ則の双線型評価について、高階の積分表示を新たに見出すことにより、完全な展開式と最良の剰余評価を得た。

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

研究計画は予定通り順調に進んでいる。現在までの研究で思いがけない着想が幾つか得られており、今後の進展に繋がる事が期待される。

Strategy for Future Research Activity

現在までの研究が順調に進展しているので、今後の推進方策に大きな変更は無い。

Causes of Carryover

図書などの洋書や物品費、旅費が当初の予定よりも安価で済み、次年度使用額が生じた。

Expenditure Plan for Carryover Budget

研究発表及び分担者との研究グループ強化のための旅費に加える計画である。

  • Research Products

    (18 results)

All 2017 2016 Other

All Int'l Joint Research (1 results) Journal Article (6 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 6 results,  Acknowledgement Compliant: 2 results) Presentation (9 results) (of which Int'l Joint Research: 9 results,  Invited: 9 results) Book (1 results) Remarks (1 results)

  • [Int'l Joint Research] バーミンガム大学(英国)

    • Country Name
      UNITED KINGDOM
    • Counterpart Institution
      バーミンガム大学
  • [Journal Article] Ground states for semi-relativistic Schr¨odinger-Poisson-Slater energy2017

    • Author(s)
      J. Bellazzini, T. Ozawa, N. Visciglia
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Higher order fractional Leibniz rule2017

    • Author(s)
      K. Fujiwara, V. Georgiev, T. Ozawa
    • Journal Title

      J. Fourier Anal.Appl.

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Behaviour of the Brascamp-Lieb constant2017

    • Author(s)
      J. Bennett, N. Bez, M. Cowling, T. Flock
    • Journal Title

      Bulletin of the London Mathematical Society

      Volume: 印刷中 Pages: 印刷中

    • DOI

      10.1112/blms.12049

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Stability of the Brascamp-Lieb constant and applications2017

    • Author(s)
      J. Bennett, N. Bez, T. Flock, S. Lee
    • Journal Title

      The American Journal of Mathematics

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Estimates for the kinetic transport equation in hyperbolic Sobolev spaces2017

    • Author(s)
      J. Bennett, N. Bez, S. Gutierrez, S. Lee
    • Journal Title

      Journal de Math'ematiques Pures et Appliqu'ees

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Sharp lower bounds for Coulomb energy2016

    • Author(s)
      J. Bellazzini, M. Ghimenti, T. Ozawa
    • Journal Title

      Math. Research Letters

      Volume: 23 Pages: 621-632

    • DOI

      http://dx.doi.org/10.4310/MRL.2016.v23.n3.a2

    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Stability of the Brascamp-Lieb inequality2017

    • Author(s)
      Neal Bez
    • Organizer
      Analysis Seminar
    • Place of Presentation
      University of Edinburgh (イギリス・エジンバラ)
    • Year and Date
      2017-03-20
    • Int'l Joint Research / Invited
  • [Presentation] Smoothing estimates for the kinetic transport equation via the cone multiplier2017

    • Author(s)
      Neal Bez
    • Organizer
      Harmonic Analysis Workshop
    • Place of Presentation
      金沢大学 (石川県・金沢市)
    • Year and Date
      2017-03-05
    • Int'l Joint Research / Invited
  • [Presentation] Smoothing estimates for velocity averages via the cone multiplier2017

    • Author(s)
      Neal Bez
    • Organizer
      Harmonic Analysis and Applications Conference
    • Place of Presentation
      Seoul National University (韓国・ソウル)
    • Year and Date
      2017-03-01
    • Int'l Joint Research / Invited
  • [Presentation] Stability of the Brascamp-Lieb constant and applications2016

    • Author(s)
      Neal Bez
    • Organizer
      International Conference for the 70th Anniversary of the Korean Mathematical Society
    • Place of Presentation
      Seoul National University (韓国・ソウル)
    • Year and Date
      2016-10-22
    • Int'l Joint Research / Invited
  • [Presentation] Uncertainty relations in the framework of equalities2016

    • Author(s)
      Tohru Ozawa
    • Organizer
      International Conference for the 70th Anniversary of Korean Mathematical Society
    • Place of Presentation
      Seoul National University (韓国・ソウル)
    • Year and Date
      2016-10-20 – 2016-10-23
    • Int'l Joint Research / Invited
  • [Presentation] Estimates for the kinetic transport equation in hyperbolic Sobolev spaces2016

    • Author(s)
      Neal Bez
    • Organizer
      Analysis Seminar
    • Place of Presentation
      Seoul National University (韓国・ソウル)
    • Year and Date
      2016-10-19
    • Int'l Joint Research / Invited
  • [Presentation] Uncertainty relations in the framework of equalities2016

    • Author(s)
      Tohru Ozawa
    • Organizer
      New trends in Partial Differential Equations
    • Place of Presentation
      Centro di Ricerca Matematica Ennio De Giorgi (イタリア・ピサ)
    • Year and Date
      2016-10-03 – 2016-10-07
    • Int'l Joint Research / Invited
  • [Presentation] Higher order fractional Leibniz estimates2016

    • Author(s)
      Tohru Ozawa
    • Organizer
      Nonlinear Wave and Dispersive Equations, Kyoto 2016
    • Place of Presentation
      京都大学 (京都府・京都市左京区)
    • Year and Date
      2016-09-06 – 2016-09-08
    • Int'l Joint Research / Invited
  • [Presentation] 等式の枠組から観た不確定性関係2016

    • Author(s)
      Tohru Ozawa
    • Organizer
      微分方程式セミナー Seminar of Differential Equations
    • Place of Presentation
      大阪大学 数学教室 大セミナー室(E301) (大阪府・豊中市)
    • Year and Date
      2016-06-10
    • Int'l Joint Research / Invited
  • [Book] 数理物理学としての微分方程式序論2016

    • Author(s)
      小澤徹
    • Total Pages
      192
    • Publisher
      サイエンス社
  • [Remarks] 小澤徹研究室

    • URL

      http://www.ozawa.phys.waseda.ac.jp/index2.html

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Published: 2018-01-16   Modified: 2022-02-21  

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