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Studies on complex analysis for pseudoconvex domains of finite type

Research Project

Project/Area Number 22540199
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KAMIMOTO Joe  九州大学, 数理(科)学研究科(研究院), 准教授 (90301374)

Research Collaborator NOSE Toshihiro  九州産業大学, 工学部, 特認講師 (90637993)
Project Period (FY) 2010-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords有限型擬凸領域 / 正則関数 / 境界挙動 / ピーク関数 / ベルグマン核 / 振動積分 / 局所ゼータ関数 / ニュートン多面体 / 有限型領域 / セゲー核 / タイプ / 特異点解消 / トーリック多様体 / 漸近展開 / バンピング / Bergman核 / Peak関数 / 特異点論
Outline of Final Research Achievements

In the study of several complex variables, it is very important to understand the boundary behavior of holomorphic functions. I precisely studied this subject. In particular, I am interested in the case when the domain satisfies the finite type condition. In this investigation, the concept of Newton polyhedra, which is important in the study of singularity theory, reflects these investigations. On the other hands, I also study the asymptotic analysis of oscillatory integrals and local zeta functions, which are closely related to the above mentioned studies.

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

    (19 results)

All 2015 2014 2013 2012 2011

All Journal Article (12 results) (of which Peer Reviewed: 10 results,  Open Access: 1 results,  Acknowledgement Compliant: 1 results) Presentation (7 results) (of which Invited: 6 results)

  • [Journal Article] Newton polyhedra and weighted oscillatory integrals with smooth phases2015

    • Author(s)
      Joe Kamimoto and Toshihiro Nose
    • Journal Title

      Transaction of Amer. Math. Soc.

      Volume: 未定

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] On meromorphic continuation of local zeta functions,2015

    • Author(s)
      Joe Kamimoto and Toshihiro Nose
    • Journal Title

      Proceedings of KSCV10

      Volume: 未定

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 多変数関数論における解析接続2014

    • Author(s)
      神本 丈
    • Journal Title

      数理科学

      Volume: 616 Pages: 52-57

    • Related Report
      2014 Annual Research Report
  • [Journal Article] Asymptotic analysis of oscillatory integrals via the Newton polyhedra of the phase and the amplitude2013

    • Author(s)
      Koji Cho, Joe Kamimoto and Toshihiro Nose
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 65 Issue: 2 Pages: 521-562

    • DOI

      10.2969/jmsj/06520521

    • NAID

      10031177290

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On oscillatory integrals with C^{\infty} phases2013

    • Author(s)
      Joe Kamimoto and Toshihiro Nose
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B40 Pages: 31-40

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic analysis of oscillatory integrals via the Newton polyhedra of the phase and the amplitude2013

    • Author(s)
      K. Cho、J. Kamimoto and T. Nose
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 65 Pages: 1-42

    • NAID

      10031177290

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic anaysis of weighted oscillatory integrals via Newton polyhedra2013

    • Author(s)
      J. Kamimoto and T. Nose
    • Journal Title

      Proceedings of the 19th ICFIDCAA Hiroshima 2011, Tohoku University Press, Sendai

      Volume: なし Pages: 3-12

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On oscillatory integrals with $C^{\infty}$ phases2013

    • Author(s)
      J. Kamimoto and T. Nose
    • Journal Title

      RIMS K\^oky\^uroku Bessatsu

      Volume: B40 Pages: 31-40

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic analysis of oscillatory integrals via Newton polyhedra of the phase and the amplitude2012

    • Author(s)
      K.Cho, J.Kamimoto, T.Nose
    • Journal Title

      Journal of Math.Soc.of Japan

      Volume: (未定)

    • NAID

      10031177290

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic analysis of oscillatory integrals and local zeta functions2012

    • Author(s)
      J.Kamimoto, T.Nose
    • Journal Title

      京大数理解析研究所考究録

      Volume: (未定)

    • Related Report
      2011 Annual Research Report
  • [Journal Article] ASYMPTOTICS OF THE BERGMAN FUNCTION FOR SEMIPOSITIVE HOLOMORPHIC LINE BUNDLES2011

    • Author(s)
      K.Cho, J.Kamimoto, T.Nose
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 65 Issue: 2 Pages: 349-382

    • DOI

      10.2206/kyushujm.65.349

    • NAID

      130001444151

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotics of the Bergman function for semipositive holonorphic line bundle2011

    • Author(s)
      K.Cho, J.Kamimoto, T.Nose
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: (掲載予定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] On local zeta functions in two dimensions2014

    • Author(s)
      神本 丈
    • Organizer
      研究集会「超局所解析の諸相」
    • Place of Presentation
      京都大学数理解析研
    • Year and Date
      2014-10-23
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Newton polyhera and oscillatory integrals2014

    • Author(s)
      Joe Kamimoto
    • Organizer
      代数・幾何・解析セミナー
    • Place of Presentation
      鹿児島大学理学部
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Resolution of singularities via Newton polyhedra and its applications to analysis2014

    • Author(s)
      Joe Kamimoto
    • Organizer
      複素解析セミナー
    • Place of Presentation
      東京大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Newton polyhedra and oscillatory integrals2013

    • Author(s)
      神本 丈
    • Organizer
      HMAセミナー・冬の研究会,広島大学
    • Place of Presentation
      広島大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] On oscillatory integrals with smooth phases2012

    • Author(s)
      Joe Kamimoto
    • Organizer
      ``Geometric Complex Analysis Tokyo 2012''
    • Place of Presentation
      東京大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] ニュートン多面体とベルグマン核の漸近解析2012

    • Author(s)
      神本 丈
    • Organizer
      第55回函数論シンポジウム,金沢大学サテライト・プラザ
    • Place of Presentation
      金沢大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Newton polyhedra and oscillatory integrals2011

    • Author(s)
      Joe Kamimoto
    • Organizer
      The 19^<th> International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      アスタープラザ広島(招待講演)
    • Year and Date
      2011-12-12
    • Related Report
      2011 Annual Research Report

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Published: 2010-11-30   Modified: 2019-07-29  

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