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2008 Fiscal Year Final Research Report

Singularities of solutions to Schrodinger equations

Research Project

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Project/Area Number 17340033
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionThe University of Tokyo

Principal Investigator

NAKAMURA Shu  The University of Tokyo, 大学院・数理科学研究科, 教授 (50183520)

Project Period (FY) 2005 – 2008
Keywords偏微分方程式 / 量子力学 / 超局所解析
Research Abstract

シュレディンガー方程式の解の特異性の伝播に関する研究を行い、特に、非束縛的な仮定の下で、解の超局所特異性を古典力学的散乱理論を用いて特徴づけることに成功した。この成果は、当初はユークリッド空間上の短距離型摂動の場合に証明され、さらに長距離型摂動、散乱多様体、摂動を持つ調和振動子、また解析的特異性の特徴付けへと拡張された。また、実解析的な平滑化作用に関する研究成果も得た。

  • Research Products

    (29 results)

All 2009 2008 2007 2006 2005 Other

All Journal Article (16 results) (of which Peer Reviewed: 16 results) Presentation (13 results)

  • [Journal Article] Wave front set for solutions to Schrodinger equations2009

    • Author(s)
      Nakamura, S.
    • Journal Title

      J.Functional Analysis 256

      Pages: 1299-1309

    • Peer Reviewed
  • [Journal Article] Semiclassical singular-ity propagation property for Schrodinger equations2009

    • Author(s)
      Nakamura, S.
    • Journal Title

      J. Math. Soc. Japan 61

      Pages: 177-211

    • Peer Reviewed
  • [Journal Article] Spectral extrema and Lifshitz tails for non monotonous alloy type models2009

    • Author(s)
      Klopp, F., Nakamura,S.
    • Journal Title

      Commun. Math. Phys 287

      Pages: 1133-1143

    • Peer Reviewed
  • [Journal Article] Wave front set for solutions to perturbed harmonic oscillators. Comm2009

    • Author(s)
      Mao, S., Nakamura, S.
    • Journal Title

      Partial Differential Equations 34

      Pages: 506-519

    • Peer Reviewed
  • [Journal Article] Analytic singularities for long range Schrodinger equations2008

    • Author(s)
      Martinez, A., Nakamura, S., Sordoni, V.
    • Journal Title

      Comptes Rendus Mathematique 346, 15-16

      Pages: 849-852

    • Peer Reviewed
  • [Journal Article] On Lp bounded-ness of wave operators for 4-dimensional Schrodinger operators with threshold singularities2008

    • Author(s)
      Jensen, A., Yajima, K.
    • Journal Title

      Proc. Lond. Math. Soc 86

      Pages: 136-162

    • Peer Reviewed
  • [Journal Article] Analytic Smoothing Effect for the Schrodinger Equation with Long-Range Perturbation, Comm2006

    • Author(s)
      Martinez, A., Nakamura, S., Sordoni, V.
    • Journal Title

      Pure Appl. Math 59

      Pages: 1330-1351

    • Peer Reviewed
  • [Journal Article] Bounds on the spectral shift function and the density of states2006

    • Author(s)
      Hundertmark, D., Killip, R., Nakamura, S., Stollmann, P., Veselic, I..
    • Journal Title

      Commun. Math. Phys 262

      Pages: 489-503

    • Peer Reviewed
  • [Journal Article] The L^p boundedness of wave operators for Schrodinger operators with threshold singularities2006

    • Author(s)
      Yajima, K.
    • Journal Title

      I.. The odd dimensional case. J. Math. Sci. Univ. Tokyo 13

      Pages: 43-93

    • Peer Reviewed
  • [Journal Article] The L^p bounded-ness of wave operators for Schrodinger operators with threshold singularities.II. Even dimensional case2006

    • Author(s)
      Finco, D., Yajima,K.
    • Journal Title

      J. Math. Sci.Univ. Tokyo 13

      Pages: 277-346

    • Peer Reviewed
  • [Journal Article] Propagation of singularities for Schrodinger equations on the Euclidean space with a scattering metric2006

    • Author(s)
      Ito, K.
    • Journal Title

      Comm. Partial Differential Equations 31

      Pages: 1735-1777

    • Peer Reviewed
  • [Journal Article] Propagation of the homogeneous wave front set for Schrodinger equations2005

    • Author(s)
      Nakamura, S
    • Journal Title

      Duke Math. J 126

      Pages: 349-367

    • Peer Reviewed
  • [Journal Article] Dispersive estimates for Schrodinger equations with threshold resonance and eigenvalue2005

    • Author(s)
      Yajima, K.
    • Journal Title

      Comm. Math. Phys 259

      Pages: 475-509

    • Peer Reviewed
  • [Journal Article] Smoothness of solutions for Schrodinger equations with unbounded potentials2005

    • Author(s)
      Doi, S.
    • Journal Title

      Publ. Res. Inst. Math. Sci 41

      Pages: 175-221

    • Peer Reviewed
  • [Journal Article] Singularities of solutions to Schrodinger equation on scattering manifold

    • Author(s)
      Ito, K., Nakamura, S.
    • Journal Title

      American J. Math (印刷中)

    • Peer Reviewed
  • [Journal Article] Analytic wave front for solutions to Schrodinger equation

    • Author(s)
      Martinez, A., Nakamura, S., Sordoni, V.
    • Journal Title

      Advances in Math (印刷中)

    • Peer Reviewed
  • [Presentation] Time-dependent scattering theory for Schrodinger operators on scattering manifolds2008

    • Author(s)
      中村周
    • Organizer
      BIRS Workshop : Mathematical Theory of Resonances. Banff
    • Place of Presentation
      Canada
    • Year and Date
      2008-10-23
  • [Presentation] Propagation of singularities for Schrodinger operators2008

    • Author(s)
      中村周
    • Organizer
      Second Symposium on Scattering and Spectral Theory, Serrambi
    • Place of Presentation
      Brazil
    • Year and Date
      2008-08-21
  • [Presentation] Lifshitz tails for non monotonous alloy type model2008

    • Author(s)
      中村周
    • Organizer
      Oberwolfach Workshop : Disordered Systems : Random Schrodinger Operators and Random Matrices,Oberwolfach
    • Place of Presentation
      Germany
    • Year and Date
      2008-03-28
  • [Presentation] Remarks on scattering on scattering manifold2008

    • Author(s)
      中村周
    • Organizer
      研究集会「スペクトル・散乱理論とその周辺」(京都大学・数理解析研究所)
    • Year and Date
      2008-01-16
  • [Presentation] Singularity of solutions to Schrodinger equation on scattering manifold2007

    • Author(s)
      中村周
    • Organizer
      Mathematical Physics Seminar at Inst.H. Poincare
    • Place of Presentation
      Paris
    • Year and Date
      2007-07-31
  • [Presentation] Singularity of solutions to Schrodinger equation on scattering manifold2007

    • Author(s)
      中村周
    • Organizer
      Seminar at Euler Institute
    • Place of Presentation
      St.Petersburg
    • Year and Date
      2007-07-31
  • [Presentation] Singularity of solutions to Schrodinger equation on scattering manifold2007

    • Author(s)
      中村周
    • Organizer
      Seminar at Univ. Bologna
    • Year and Date
      2007-06-04
  • [Presentation] Topics on scattering theory for Schrodinger operators2007

    • Author(s)
      中村周
    • Organizer
      Seminar at Univ
    • Place of Presentation
      Paris
    • Year and Date
      2007-05-29
  • [Presentation] シュレディンガー方程式の解の特異性とその周辺2007

    • Author(s)
      中村周
    • Organizer
      日本数学会年会・企画特別講演
    • Place of Presentation
      埼玉大学
    • Year and Date
      2007-03-30
  • [Presentation] Singularity of solutions to Schrodinger equations2006

    • Author(s)
      中村周
    • Organizer
      International Conference : Spectral Theory of Random Operators and Related Fields in Probability Theory
    • Place of Presentation
      Kyoto Univ
    • Year and Date
      2006-12-11
  • [Presentation] Singularity of solutions to Schrodinger equations2006

    • Author(s)
      中村周
    • Organizer
      Seminar at Dept.Math., The Australian National University
    • Place of Presentation
      Canberra, Australia
    • Year and Date
      2006-10-30
  • [Presentation] Singularity of solutions to Schrodinger equation with variable coefficients2006

    • Author(s)
      中村周
    • Organizer
      PASI(Pan-American Advanced Studies Institute)
    • Place of Presentation
      Santiago, Chile
    • Year and Date
      2006-07-31
  • [Presentation] Semiclassical singularity propagation property for Schrodinger equation with long-range perturbation2006

    • Author(s)
      中村周
    • Organizer
      BIRS Workshop : Schrodinger Evolution Equations, Banff
    • Place of Presentation
      Canada
    • Year and Date
      2006-04-23

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Published: 2010-06-10   Modified: 2016-04-21  

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