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Study of multi-microlocalization and its applications

Research Project

Project/Area Number 15K04887
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionHokkaido University

Principal Investigator

Honda Naofumi  北海道大学, 理学研究院, 教授 (00238817)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords超局所解析 / 多重特殊化 / 多重超局所解析 / チェックドルボーコホモロジー / 代数解析 / 多重超局所化
Outline of Final Research Achievements

Multi-microlocalization is a method which enables us to microlocalize an object along several manifolds simultaneously. The purpose of this research is to extend this mothod to more general cases, and then, to establish a theory of multi-microlocal operators.
In the first two years of our research, we studied generalization of multi-specialization and succeeded in constructing multi-specialization for a general family of submanifolds located suitably. During the rest of the period, we studied applications of Cech-Dolbeault cohomology theory to the theory of hyperfunctions. We had several interesting results, which suggested us that the theory is very effective for a construction of multi-microlocal operators too.

Report

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

    (13 results)

All 2018 2017 2016 2015

All Journal Article (11 results) (of which Int'l Joint Research: 7 results,  Peer Reviewed: 8 results,  Open Access: 1 results,  Acknowledgement Compliant: 3 results) Book (1 results) Funded Workshop (1 results)

  • [Journal Article] Laplace hyperfunctions in several variables2018

    • Author(s)
      Naofumi Honda and Kohei Umeta
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 70 Issue: 1 Pages: 111-139

    • DOI

      10.2969/jmsj/07017267

    • NAID

      130006334097

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Foundation of symbol theory for analytic pseudodifferential operators, I2017

    • Author(s)
      Takashi Aoki, Naofumi Honda and Susumu Yamazaki
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 69 Issue: 4 Pages: 1715-1801

    • DOI

      10.2969/jmsj/06941715

    • NAID

      130006887116

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Generalization of multi-specializations and multi-asymptotics2017

    • Author(s)
      Naofumi Honda and Luca Prelli
    • Journal Title

      RIMS講究録

      Volume: 2020 Pages: 18-28

    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Journal Article] Apparent parameter technique and vanishing of cohomology groups with Whitney holomorphic functions2017

    • Author(s)
      Naofumi Honda
    • Journal Title

      RIMS講究録

      Volume: 2020 Pages: 10-17

    • Related Report
      2017 Annual Research Report
  • [Journal Article] On the theory of Laplace hyperfunctions in several variables2017

    • Author(s)
      Naofumi Honda and Kouhei Umeta
    • Journal Title

      RIMS講究録

      Volume: 2020 Pages: 29-34

    • Related Report
      2017 Annual Research Report
  • [Journal Article] A study of pinch points and cusps in the Landau-Nakanishi geometry2016

    • Author(s)
      Naofumi Honda and Takahiro Kawai
    • Journal Title

      Kokyuroku Bessatsu, RIMS

      Volume: B57 Pages: 195-234

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Multi-microlocalization2016

    • Author(s)
      Naofumi Honda, Luca Prelli and Susumu Yamazaki
    • Journal Title

      Kokyuroku Bessatsu, RIMS

      Volume: B57 Pages: 93-116

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Multi-microlocalization and microsupport2016

    • Author(s)
      Naofumi Honda, Luca Prelli and Susumu Yamazaki
    • Journal Title

      Bulletin de la Socie'te' Mathe'matique de France

      Volume: 144 Pages: 569-611

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On the geometric aspect of Sato's postulates on the S-matrix2015

    • Author(s)
      N. Honda, T. Kawai and H. P. Stapp
    • Journal Title

      RIMS Koukyuroku Bessatsu

      Volume: B52 Pages: 11-53

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Kernel functions and symbols of pseudodifferential operators of infinite order with an apparent parameter2015

    • Author(s)
      T. Aoki, N.Honda and S.Yamazaki
    • Journal Title

      RIMS Koukyuroku Bessatsu

      Volume: B52 Pages: 175-192

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On the sheaf of Laplace hyperfunctions in several variables2015

    • Author(s)
      N. Honda and K. Umeta
    • Journal Title

      RIMS Koukyuroku Bessatsu

      Volume: B52 Pages: 213-218

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Book] Virtual turning points2015

    • Author(s)
      N. Honda, T.Kawai and Y.Takei
    • Total Pages
      126
    • Publisher
      Springer
    • Related Report
      2015 Research-status Report
  • [Funded Workshop] New development of microlocal analysis and singular perturbation theory2016

    • Place of Presentation
      Kyoto University, RIMS (京都府、 京都市)
    • Year and Date
      2016-10-03
    • Related Report
      2016 Research-status Report

URL: 

Published: 2015-04-16   Modified: 2019-03-29  

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