Exact WKB analysis for simple-pole type oprators

• Project/Area Number: 18740071
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kobe University (2007-2008); Kyoto University (2006)
• Principal Investigator: KOIKE Tatsuya Kobe University, 大学院理学研究科, 准教授 (80324599)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,840,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000); Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 完全WKB 解析 / Borel 和 / 漸近解析 / 単純極型作用素 / 完全WKB解析 / クーロンポテンシャル / Voros係数 / 関数方程式論

Research Abstract

完全WKB 解析における単純極型作用素の問題に取り組み、高階単純極型作用素の分解定理について論じた。
特に、係数が全て単純極であるような一番簡単な場合は二階の単純極型作用素と正則係数作用素に分解できることを示し、それを用いて単純極を端点とするStokes 曲線での接続係数を決定した。
それ以外の場合についても分解して得られる二階の単純極型作用素の決定を行なうなど、特異点における解析の進展に寄与した。

Research Products

• [Journal Article] On new expressions of the Painlev´e hierarchies (2008)
  • Author(s): T. Koike
  • Journal Title: K?oky?uroku Bessatsu B5 Pages: 153-198
  • Peer Reviewed
• [Journal Article] Virtual Turning Points ? A gift of microlocal analysis to the exact WKB analysis, Algebraic Analysis of Differential Equations (2008)
  • Author(s): T. Aoki, N. Honda, T. Kawai, T. Koike, Y. Nishikawa, S. Sasaki, A. Shudo, Y. Takei
  • Journal Title: Springer Pages: 29-43
  • Peer Reviewed
• [Journal Article] On new expressions of the Painleve hierarchies (2008)
  • Author(s): T. Koike
  • Journal Title: Kokyuroku Bessatsu B5 Pages: 153-198
  • Peer Reviewed
• [Journal Article] On the Hamiltonian structures of the second and the fourth Painlev´e hierarchies and degenerate Garnier systems (2007)
  • Author(s): T. Koike
  • Journal Title: K?oky?uroku Bessatsu B2 Pages: 99-127
  • Peer Reviewed
• [Journal Article] On the Hamiltonian structures of the second and the fourth Painleve hierarchies and degenerate Garnier systems (2007)
  • Author(s): T. Koike
  • Journal Title: Kokyuroku Bessatsu B2 Pages: 99-127
  • Peer Reviewed
• [Journal Article] On the Hamiltonian structures of the second and the fourth Painleve hierarchies and degenerate Garnier systems. (2007)
  • Author(s): Tatsuya Koike
  • Journal Title: RIMS Kokyuroku Bessatsu B2 Pages: 99-127
• [Presentation] On the explicit forms of the Voros coefficients of the Coulomb potential in exact WKB analysis (2009)
  • Author(s): 小池達也
  • Organizer: 超幾何方程式研究会2009 一般講演
  • Place of Presentation: 神戸大学
  • Year and Date: 2009-01-07
• [Presentation] Asymptotic behavior of the hyperbolic Schwarz map at irregular singular points (joint work with T. Sasaki and M. Yoshida) (2008)
  • Author(s): T. Koike
  • Organizer: Foundations of exact WKB analysis and resurgence theory
  • Place of Presentation: 関西セミナーハウス
  • Year and Date: 2008-12-15
• [Presentation] On the explicit forms of the Voros coefficients of the Coulomb potential in exact WKB analysis (2008)
  • Author(s): T. Koike
  • Organizer: Seminar on Singular Perturbations
  • Place of Presentation: Special weeks on parametric resurgence、京都大学
  • Year and Date: 2008-09-29
• [Presentation] Painlev´e hierarchies, degenerate Garnier systems and WKB analysis (2008)
  • Author(s): 小池達也
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 特別講演, 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] Painleve hierarchies, degenerate Gamier systems and WKB analysis (2008)
  • Author(s): 小池達せ
  • Organizer: 日本学会秋季総合分科会函数方程式論分科会特別講演
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] On the explicit forms of the Voros coefficients of the Coulomb potential in exact WKB analysis Workshop on New approach to analytic equations ? transformation theory (2008)
  • Author(s): T. Koike
  • Organizer: singular solutions and Stokes problem
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-09-18
• [Presentation] On the eigenvalue problem of the Coulomb potential and exact WKB analysis, InternationalWorkshop on Global Behaviors of Differential Equations (2008)
  • Author(s): T. Koike
  • Organizer: Singularity and Transformation Theory?
  • Place of Presentation: 広島大学理学研究科,
  • Year and Date: 2008-09-10
• [Presentation] On the eigenvalue problem of the Coulomb potential and exact WKB analysis (2008)
  • Author(s): 小池達也
  • Organizer: International Workshop on Global Behayiors of Differential Equations
  • Place of Presentation: 広島大学
  • Year and Date: 2008-09-10
• [Presentation] P^34-hierarchy, degenerate Garnier systems and WKB analysis. 研究集会「完全WKB 解析と超局所解析 (2008)
  • Author(s): T. Koike
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-05-27
• [Presentation] クーロンポテンシャルに対する固有値問題と完全WKB 解析, (2008)
  • Author(s): 小池達也
  • Organizer: 九州大学大学院数理科学研究院談話会
  • Place of Presentation: 九州大学
  • Year and Date: 2008-04-23
• [Presentation] On the eigenvalue problem of the Coulomb potential and exact WKB analysis Holomorphic partial differential equations (2008)
  • Author(s): T. Koike
  • Organizer: small divisors and summability
  • Place of Presentation: CIRM(フランス)
  • Year and Date: 2008-01-29
• [Presentation] On the eigenvalue problem of the Coulomb potential and excact WKB analysis (2008)
  • Author(s): T. Koike
  • Organizer: Holomorphic partial differential equations, small divisors and summability
  • Place of Presentation: CIRM, France
  • Year and Date: 2008-01-29
• [Presentation] 単純極型作用素の完全WKB 解析について (2008)
  • Author(s): 小池達也
  • Organizer: 超幾何方程式研究会2008
  • Place of Presentation: 神戸大学
  • Year and Date: 2008-01-07
• [Presentation] 単純極型作用素の完全WEB解析について (2008)
  • Author(s): T. Koike
  • Organizer: 超幾何方程式研究会2008
  • Place of Presentation: 神戸大学,日本
  • Year and Date: 2008-01-07
• [Presentation] On Painlev´e hierarchies and the degenerate Garnier systems (2007)
  • Author(s): T. Koike
  • Organizer: Differential Equations and Asymptotic Analysis
  • Place of Presentation: 京都大学数理解析研究所,
  • Year and Date: 2007-12-17
• [Presentation] On Painleve hierarchies and the degenerate Garnier systems (2007)
  • Author(s): T. Koike
  • Organizer: Differential Equations and Asymptotic Analysis
  • Place of Presentation: 数理解析研究所,日本
  • Year and Date: 2007-12-17
• [Presentation] Higher order Painlev´e equations and the degenerate Garnier systems (2007)
  • Author(s): T. Koike
  • Organizer: 微分方程式系の代数解析と完全WKB 解析
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2007-12-13
• [Presentation] クーロンポテンシャルに対する固有値問題と完全WKB 解析 (2007)
  • Author(s): 小池達也
  • Organizer: 神戸大学理学研究科数学教室談話会
  • Place of Presentation: 神戸大学
  • Year and Date: 2007-10-31
• [Presentation] On the Hamiltonian representation of the second and fourth Painlev´e hierarchies (2006)
  • Author(s): 小池達也:
  • Organizer: 京都解析コロキウム
  • Place of Presentation: 京都大学
  • Year and Date: 2006-06-17
• [Presentation] On the Hamiltonian representation of the second and fourth Painlev´e hierarchies (2006)
  • Author(s): T. Koike
  • Organizer: 平成18 年度日仏セミナー「Algebraic, Analytic and Geometric Aspects of Complex Differential Equations and their Deformations, Painlev´e Hierarchies
  • Place of Presentation: 京都大学数理解析研究所,
  • Year and Date: 2006-05-16