Analytic Integral and its applications

解析积分及其应用

• 批准号: 11440041
• 负责人: MIYAKE Masatake
• 金额: $ 6.53万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11440041/
• 关键词: quasi hypergeometric; LR transform; orthogonal polynomials; divergent solution; Borel summability; singular equation; 形式的巾級数解; 収束,発散; ポアンカレ条件; ジュブレイ指数; 接続関係式; 超球面配置; 超幾何積分; 差分方程式; 接続行列; Wu方程式; 特異点; モノドロミー; 離散可積分系

K.Aomoto studied integral representation of special functions and obtained the following results :1) He established an integral formulas for quasi hypergeometric functions and obtained monodromy formulas, and gave an explicit formula of singular point by using Picard-Lefschetz transform.2) He extended the notion of LR transform and density matrices into multi dimensional case. More explicitly, he defined Gram-Schmidt orthogonal polynomials with a given density and he dfined its LR transform.M.Miyake studied partial differential equatons in complex domain and obtained the following results :3) He characterized the Borel summability of divergent formal solution of the Cauchy problem of certain non-Kowalevski type equations. He also gave an integral representation of the Borel sum.4) He characterized a notion of singular equation or singular point for a nonlinear partial differential equation which depends on each solution. Moreover, the characterization of the singulaity is given by showing the convergent or the divergent criterion of the formal solutions.

K.Aomoto研究了特殊函数的积分表示，得到了以下结果：1)建立了拟超几何函数的积分公式，得到了一元公式，并利用Picard-Lefschetz变换给出了奇异点的显式公式。2)他将LR变换和密度矩阵的概念推广到多维情况。更明确地，他定义了给定密度的g - schmidt正交多项式，并定义了它的LR变换。m.m iyake研究了复域上的偏微分方程，得到了以下结果：3)刻画了一类非kowalevski型方程的Cauchy问题的发散形式解的Borel可和性。他还给出了Borel和的积分表示。他提出了一个非线性偏微分方程的奇异方程或奇异点的概念，它依赖于每一个解。此外，通过给出形式解的收敛判据或发散判据，给出了奇异性的表征。

项目成果

K.AOMOTO: "Density matrices and LR Transforms"RIMS Koukyuroku. 1227. 14-60 (2001)

K.AOMOTO：“密度矩阵和 LR 变换”RIMS Koukyuroku。

K.AOMOTO: "Integral nemesentation of quali-hynergeanetric fanctions"Proc.of Hong-Kong Workshop. 1-15 (2000)

K.AOMOTO：“Integral nemementation of quali-hynergeanetric fanctions”Proc.of Hong-Kong Workshop。

M.MIYAKE: "Borel summability of divergent solutions of the Candy problem to non-Kowalevskian equations"Partial differential equations and their applications (Wuhan,1999). 225-239 (1999)

M.MIYAKE：“Candy问题对非Kowalevskian方程的发散解的Borel可求和性”偏微分方程及其应用（武汉，1999）。

K.Aomoto: "Integrable system of the heat kernel associated with logarithmic potentials"Annales Polonic Mat.. 74. 51-64 (2000)

K.Aomoto：“与对数势相关的热核的可积系统”Annales Polonic Mat.. 74. 51-64 (2000)

Kazuhiko AOMOTO: "Twistor integral representation"Journal of Geometry and Physics. 32. 189-210 (1999)

Kazuhiko AOMOTO：“扭转积分表示”几何与物理杂志。