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Asymptotic analysis in harmonic analysis by using Newton polyhedra

Research Project

Project/Area Number 15K17565
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionFukuoka Institute of Technology (2016-2017)
Kyushu Sangyo University (2015)

Principal Investigator

NOSE Toshihiro  福岡工業大学, 工学部, 助教 (90637993)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywordsニュートン多面体 / 振動積分 / 局所ゼータ関数 / トーリック・ブローアップ / 特異点解消 / 漸近解析 / 解析接続
Outline of Final Research Achievements

(1) We study toric blowing-ups related to Newton polyhedra. Using the blowing-ups, we locally represent the zero variety of smooth functions in simplified forms in two-dimensional cases. (2) We investigate the asymptotic behavior of oscillatory integrals with smooth phases in two dimensions. We have very interesting results such as log terms appearing in asymptotic limit of oscillatory integrals. (3) We show that local zeta functions can not be analytically continued as meromorphic functions across some point in some two dimensional smooth setting. In more general case, the region to which local zeta functions can be analytically continued as meromorphic functions are estimated by some geometrical information of Newton polyhedra.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (9 results)

All 2017 2016 2015

All Journal Article (3 results) (of which Peer Reviewed: 3 results,  Open Access: 1 results) Presentation (6 results) (of which Int'l Joint Research: 3 results,  Invited: 3 results)

  • [Journal Article] Asymptotic limit of oscillatory integrals with certain smooth phases2017

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

      RIMS Kokyuroku Bessatsu

      Volume: B63 Pages: 103-114

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Asymptotic limit of oscillatory integrals with certain smooth phases2017

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

      RIMS Kokyuroku Bessatsu

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] On meromorphic continuation of local zeta functions2015

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

      Complex Analysis and Geometry, Springer Proc. Math. Stat.

      Volume: 144 Pages: 187-195

    • DOI

      10.1007/978-4-431-55744-9_13

    • ISBN
      9784431557432, 9784431557449
    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] 局所ゼータ関数の解析接続と漸近解析について2017

    • Author(s)
      野瀬敏洋
    • Organizer
      第60回函数論シンポジウム
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] On the meromorphy of local zeta functions2016

    • Author(s)
      野瀬敏洋
    • Organizer
      複素解析幾何学のポテンシャル論的諸相
    • Place of Presentation
      東京大学 (東京都)
    • Year and Date
      2016-02-12
    • Related Report
      2015 Research-status Report
  • [Presentation] Failure of meromorphy of local zeta functions2016

    • Author(s)
      Toshihiro Nose
    • Organizer
      A Special SCV Day @ GAIA
    • Place of Presentation
      Pohang University of Science and Technology
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the meromorphy of local zeta functions2015

    • Author(s)
      野瀬敏洋
    • Organizer
      2015年度多変数関数論冬セミナー
    • Place of Presentation
      京都大学 (京都府京都市)
    • Year and Date
      2015-12-25
    • Related Report
      2015 Research-status Report
  • [Presentation] Meromorphic continuation of local zeta functions2015

    • Author(s)
      Toshihiro Nose
    • Organizer
      The 23rd International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      九州産業大学 (福岡県福岡市)
    • Year and Date
      2015-08-24
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] On the meromorphy of local zeta functions2015

    • Author(s)
      Toshihiro Nose
    • Organizer
      Young Mathematicians Workshop on Several Complex Variables 2015
    • Place of Presentation
      Shanghai (P.R. China)
    • Year and Date
      2015-08-10
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited

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Published: 2015-04-16   Modified: 2023-03-16  

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