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2012 Fiscal Year Final Research Report

Study of KdV hierarchy from ergode theory

Research Project

  • PDF
Project/Area Number 22540163
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKwansei Gakuin University

Principal Investigator

KOTANI Shinichi  関西学院大学, 理工学部, 教授 (10025463)

Project Period (FY) 2010 – 2012
Keywordsランダムスペクトル / 力学系 / 可積分系
Research Abstract

Segal- Wilson’s interpretation of Sato’s grassmann manifold method was applied to the closure of the space of all reflectionless potentials, and a KdV flow on it was constructed. In the construction a notion of positivity of subspaces was introduced and used to show the non-degeneracy of the τ-function. Remling’s theorem on shift flow was extended to the KdV flow by introducing generating functions and monodromy matrices describing the group action on the generating functions, which made it possible to characterize invariant subsets of the KdV flow.

  • Research Products

    (14 results)

All 2013 2012 2011 2010 Other

All Journal Article (6 results) (of which Peer Reviewed: 5 results) Presentation (7 results) Remarks (1 results)

  • [Journal Article] On the level statisticsproblem for the one-dimensional Schrodinger operator with random decaying potentials2013

    • Author(s)
      小谷眞一, 中野史彦
    • Journal Title

      数理解析研究所講究

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kenkyubu/bes satsu-j.html

    • Peer Reviewed
  • [Journal Article] Krein's strings whose spectral functions are of polynomial growth2013

    • Author(s)
      小谷眞一
    • Journal Title

      Kyoto Journal of Mathematics

    • URL

      http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&page=past&handle=eu clid.kjm

    • Peer Reviewed
  • [Journal Article] Grassmann manifold and sp ectral theory of 1D Schroedinger operato rs2011

    • Author(s)
      小谷眞一
    • Journal Title

      素粒子論研究・電子版

      Volume: Vol 10,No 1 Pages: 50-79

    • URL

      http://www2.yukawa.kyoto-u.ac.jp/~sokened/so kendenshi/vol10/yitp10_proc.pdf

  • [Journal Article] Financial inverse problem and reconstruction of infinitely divisible distributions with Gaussian co mponen2011

    • Author(s)
      小谷眞一,鍛冶俊介
    • Journal Title

      Finance and Stochastics,on line

      Pages: 1-18

    • URL

      http://link.springer.com/journal/780

    • Peer Reviewed
  • [Journal Article] Pham Van Quoc;On asymptotics of eigenvalues for a certain 1-dimensional random Schroedinger operators2011

    • Author(s)
      小谷眞一
    • Journal Title

      Osaka journal of Mathematics

      Volume: vol.48 Pages: 69-89

    • URL

      http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ojm

    • Peer Reviewed
  • [Journal Article] On limit behavior of eigenvalues spacing for I-D random Schroedinger Operators2011

    • Author(s)
      小谷眞一
    • Journal Title

      数理研講究録別冊B27

      Pages: 67-78

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kenkyubu/bes satsu-j.html

    • Peer Reviewed
  • [Presentation] A random Jacobi matrixarising from beta-ensemble2012

    • Author(s)
      小谷眞一
    • Organizer
      研究集会「ランダム作用素のスペクトルと関連する話 題」
    • Place of Presentation
      京都大学
    • Year and Date
      2012-12-06
  • [Presentation] Grassmann manifold andspectral theory of 1D Schroedingeroperators2011

    • Author(s)
      小谷眞一
    • Organizer
      Mini courses and Workshop Hilbert spaces of entire functions and spectral theory of self-adjoint differential operators
    • Place of Presentation
      CRM バルセロナ(スペイン)
    • Year and Date
      20110530-31
  • [Presentation] Infinite dimensional Grass-mann manifold on L2 and 1-D Schroe-dinger operators2011

    • Author(s)
      小谷眞一
    • Organizer
      CRM weekly seminar
    • Place of Presentation
      CRM バルセロナ(スペイン)
    • Year and Date
      2011-03-10
  • [Presentation] 1次元系の絶対連続スペクトルと可積分系2010

    • Author(s)
      小谷眞一
    • Organizer
      SummerSchool数理物理2010:「ランダムシュレーディンガー作用素」
    • Place of Presentation
      東京大学
    • Year and Date
      20100827-28
  • [Presentation] 固有値間隔の極限分布について2010

    • Author(s)
      小谷眞一
    • Organizer
      ランダム作用素のスペクトルと関連する話題
    • Place of Presentation
      慶応大学
    • Year and Date
      2010-12-09
  • [Presentation] 佐藤の可積分系理論の1次元ランダムシュレーディンガー作用素2010

    • Author(s)
      小谷眞一
    • Organizer
      基研研究会「量子科学における双対性とスケール」
    • Place of Presentation
      京都大学
    • Year and Date
      2010-11-04
  • [Presentation] KdV flow on the space of g eneralizedreflectionless potentials2010

    • Author(s)
      小谷眞一
    • Organizer
      The 2nd St.Petersburg Conference in SpectralTheory
    • Place of Presentation
      Euler International Mathematic al Institute(Russia)
    • Year and Date
      2010-07-15
  • [Remarks]

    • URL

      http://sci-tech.ksc.kwansei.ac.jp/~kotani/

URL: 

Published: 2014-08-29  

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