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Hyoellipticity and Schroedinger operators with magnetic fields

Research Project

Project/Area Number 22654019
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionUniversity of Hyogo

Principal Investigator

HOSHIRO Toshihiko  兵庫県立大学, 大学院・物質理学研究科, 教授 (40211544)

Co-Investigator(Renkei-kenkyūsha) IWASAKI Chisato  兵庫県立大学, 大学院・物質理学研究科, 教授 (30028261)
UMEDA Tomio  兵庫県立大学, 大学院・物質理学研究科, 教授 (20160319)
Project Period (FY) 2010 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥2,340,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywords偏微分方程式 / 準楕円性 / 数理物理 / スペクトル理論 / 解析学
Research Abstract

In this research, we studied hypoellipticity and the eigenvalue problems of Schroedinger operator with magnetic fields. We obtained some results on the relation between the both fields. We also organized some international conferences and supported academic exchanges between researchers related to hypoellipticity.

Report

(3 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • Research Products

    (16 results)

All 2012 2011 Other

All Journal Article (6 results) (of which Peer Reviewed: 5 results) Presentation (8 results) Remarks (2 results)

  • [Journal Article] Spectral zeta function of the sub-Laplacian on two step nilmanifolds2012

    • Author(s)
      W. Bauer-K. Furutani-C. Iwasaki
    • Journal Title

      J. Math. Pures Appl

      Volume: Vol.97 Issue: 3 Pages: 242-261

    • DOI

      10.1016/j.matpur.2011.06.003

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A sequence of zero modes of Weyl-Dirac operators and an associated sequence of solvable polynomials2012

    • Author(s)
      Y. Saito, T. Umeda
    • Journal Title

      Operator Theory : Advances and Applications

      Volume: vol.219 Pages: 197-209

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Dirac-Hardy and Dirac-Sobolev inequalities in$ L^1$2011

    • Author(s)
      A. Balinsky, W. D. Evans, T. Umeda
    • Journal Title

      Publ. RIMS

      Volume: vol.47 Pages: 791-801

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non linear eigenvalue problems and related topics2011

    • Author(s)
      T. Hoshiro
    • Journal Title

      26^<th> Matsuyama Camp : Recent Development on Partial Differential Equations

      Pages: 106-111

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Eigenfunctions at the threshold energies of magnetic Dirac operators2011

    • Author(s)
      Y. Saito, T. Umeda
    • Journal Title

      Reviews Math. Phys

      Volume: vol 23, No.2 Pages: 155-178

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non linear eigenvalue problems and related topics2011

    • Author(s)
      保城寿彦
    • Journal Title

      26^<th> Matsuyama Camp : Recent Development on Partial Differential Equations

      Volume: 1巻 Pages: 106-111

    • Related Report
      2010 Annual Research Report
  • [Presentation] A representation of the fundamental solution and eigenfunction expansion to the Fokker-Planck operator2012

    • Author(s)
      C. Iwasaki
    • Organizer
      Workshop Geometric and Singular Analysis
    • Place of Presentation
      University of Potsdam(Germany)
    • Year and Date
      2012-03-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Symbols of the fundamental solution and spectral zeta function of nilmanifolds2012

    • Author(s)
      C. Iwasaki
    • Organizer
      偏微分方程式姫路研究集会
    • Place of Presentation
      イーグレ姫路(姫路市)
    • Year and Date
      2012-02-24
    • Related Report
      2011 Final Research Report
  • [Presentation] Symbols of the fundamental solution and spectral zeta function of nilmanifolds2012

    • Author(s)
      岩崎千里
    • Organizer
      偏微分方程式姫路研究集会
    • Place of Presentation
      イーグレ姫路(兵庫県)(招待講演)
    • Year and Date
      2012-02-24
    • Related Report
      2011 Annual Research Report
  • [Presentation] Spectral zeta function of the sub-Laplacian on nilmanifolds2011

    • Author(s)
      C. Iwasaki
    • Organizer
      2011 NCTS Taiwan-Japan Joint Workshop on PDEs and SGeometric Analysis
    • Place of Presentation
      NCTS(新中、台湾)
    • Year and Date
      2011-12-21
    • Related Report
      2011 Final Research Report
  • [Presentation] A representation of the fundamental solution to the Fokker-Planck operator2011

    • Author(s)
      C. Iwasaki
    • Organizer
      Fu-Jen Form on Analysis
    • Place of Presentation
      Fu-Jen大学(台北,台湾)
    • Year and Date
      2011-12-16
    • Related Report
      2011 Final Research Report
  • [Presentation] A representation of the fundamental solution to the Fokker-Planck operator2011

    • Author(s)
      C. Iwasaki
    • Organizer
      数学教室コロキュウム
    • Place of Presentation
      University of Gottingen(Germany)
    • Year and Date
      2011-09-29
    • Related Report
      2011 Final Research Report
  • [Presentation] Non linear eigenvalue problems and related topics2011

    • Author(s)
      T. Hoshiro
    • Organizer
      26^<th> Matsuyama Camp : Recent Development on Partial Differential Equations
    • Place of Presentation
      龍谷大学ともゆき荘(京都市中京区)
    • Year and Date
      2011-01-08
    • Related Report
      2011 Final Research Report
  • [Presentation] Non linear eigenvalue problems and related topics2011

    • Author(s)
      保城寿彦
    • Organizer
      第26回松山キャンプ(26^<th> Matsuyama Camp : Recent Development on Partial Differential Equations)
    • Place of Presentation
      龍谷大学ともゆき荘(京都市中京区)
    • Year and Date
      2011-01-08
    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://web.cc.yamaguchi-u.ac.jp/~hirosawa/other/matsuyamacamp2011/lecturenotes.htm.

    • Related Report
      2010 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2016-04-21  

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