Aoki Takashi

アオキタカシ | Aoki Takashi

Research field (1)： Basic analysis

Research keywords (2)：超局所解析学 , Microlocal Analysis

Research theme for competitive and other funds (34)：

2018 - 2023 Exact WKB analysis of parametric Stokes phenomena
2014 - 2018 Algebraic analysis of parametric Stokes phenomena
2012 - 2017 The structure theory of differential equations by the algebraic analysis of singular perturbation theory
2009 - 2014 Asymptotic analysis for hypergeometric systems and Garnier systems
2010 - 2013 Asymptotic analysis of instanton-type solutions

2008 - 2012 Study of Fuchsian system of differential equations from the view point of algebraic analysis and microlocal analysis

2008 - 2011 Structure theory of higher order Painleve equations through exact WKB analysis

2006 - 2008 Exact WKB analysis of systems of differential equations

2005 - 2007 Exact WKB analysis of higher order differential equations that is centered around the notion of a virtual turning point

2005 - 2006 Algebraic study of non-local differential equations and operational calculus

2003 - 2005 Exact WKB analysis of microdifferential equations of infinite order

2003 - 2004 Algebraic-analytical Study of non-local pseudo-differential equations in complex domains

2002 - 2004 Structural analysis of differential equations by the exact WKB method

2001 - 2002 ALGEBRAIC ANALYTICAL STUDY OF SHEAVES AND INFINITE ORDRE DIFFERENTIAL EQUATIONS

2000 - 2002 WKB analysis for high-order ordinary differencial equations with a large parameter

1999 - 2001 Study on the properties for partial sums of analytic functions

1999 - 2001 Exact WKB analysis and microlocal analysis

1999 - 2000 ALGEBRAIC-ANALYTICAL STUDY OF PSEUDO-DIFFERENTIAL AND CONVOLUTION ERUATIONS

1998 - 1999 Research of rings defined by a system of differential equations

1997 - 1998 Algebraic Analysis of Exponential Asymptotics

1997 - 1998 PSEUDO-DIFFERENTIAL EQUATIONS IN COMPLEX DOMAINS

1996 - 1996 周期的シュレディンガー方程式の断熱摂動の代数解析

1995 - 1995 無限階微分方程式系のホロノミック性

1995 - 1995 パンルヴェ超越関数と指数漸近解析

1994 - 1994 無限階微分方程式系の対称性とホロノミック系

1994 - 1994 一次元可積分多体系の半古典的量子化とランダム行列模型

1993 - 1993 正則関数に関する作用素の総合的研究

1992 - 1992 擬微分作用素と異空間解析の局所的研究

1992 - 1992 モノドロミー保存変形のWKB解析

1991 - 1992 超局所解析学とS-行列理論

1991 - 1991 多変数保型形成の整数論的研究

1987 - 1987 無限階微分作用素の環の代数的研究

1986 - 1986 無限階擬微分作用素および無限階微分方程式の超局所的研究

Algebraic Analysis of Singular Perturbations

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Papers (63)：

Takashi Aoki, Toshinori Takahashi, Mika Tanda. The hypergeometric function, the confluent hypergeometric function and WKB solutions. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN. 2021. 73. 4. 1019-1062
Takashi Aoki, Kohei Iwaki, Toshinori Takahashi. Exact WKB analysisof Schrödinger equations with a Stokes curve of loop type. Funkcialaj Ekvacioj. 2019. 62. 1-34
T. Aoki, F. Colombo, I. Sabadini, D. C. Struppa. Continuity of some operators arising in the theory of superoscillations. Quantum Studies: Mathematics and Foundations. 2018. 5. 3. 463-476
T. Aoki, F. Colombo, I. Sabadini, D. C. Struppa. Continuity theorems for a class of convolution operators and applications to superoscillations. Annali di Matematica Pura ed Applicata. 2018. 197. 1-13
Takashi Aoki, Naofumi Honda, Susumu Yamazaki. Foundation of symbol theory for analytic pseudodifferential operators, I. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN. 2017. 69. 4. 1715-1801

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MISC (20)：

AOKI Takashi, HONDA Naofumi, YAMAZAKI Susumu. Kernel functions and symbols of pseudodifferential operators of infinite order with an apparent parameter (Recent development of microlocal analysis and asymptotic analysis). RIMS Kokyuroku. 2013. 1861. 156-170
AOKI Takashi, TANDA Mika. Borel sums of Voros coefficients of hypergeometric differential equations with a large parameter (Recent development of microlocal analysis and asymptotic analysis). RIMS Kokyuroku. 2013. 1861. 17-24
青木貴史, 本多尚文. 野海・山田系に付随する代数方程式系の解について (超函数と線型微分方程式 2006. 数学史とアルゴリズム). 数理解析研究所講究録. 2009. 1648. 107-116
Takashi Aoki, Hideyuki Majima, Yoshitsugu Takei, Nobuyuki Tose. Preface. Algebraic Analysis of Differential Equations: From Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai. 2008
Takashi Aoki, Hideyuki Majima, Yoshitsugu Takei, Nobuyuki Tose. Algebraic analysis of differential equations: From microlocal analysis to exponential asymptotics festschrift in honor of Takahiro Kawai. Algebraic Analysis of Differential Equations: From Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai. 2008. 1-352

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Books (4)：

Number theory--dreaming in dreams
Wrold Sci. 2009
超函数・FBI変換・無限階擬微分作用素(共著)
共立出版 2004
Instanton-type formal solutions to the second Painleve equations with a large parameter
New Trends in Microlocal Analysis(Eds. J. M. Bony, M. Morimoto), Springer 1997
WKB analysis of Painlev(]J1117[) trancendents with a large parameter, (]G0002[). - Multible-scale analysis of Painlev(]J1117[) transcendents (共著)
Structure of Solutions of Differential Equations (Eds. M. Morimoto,T.Kawai), World Scientific

Lectures and oral presentations (13)：

The hypergeometric function and WKB solutions
(15th International Symposium on Orthogonal Polynomials, Special Functions and Applications 2019)
Toward the exact WKB analysis of the generalized hypergeometric differential equation
(Workshop on Hypergeometric Equations 2019)
Toward the exact WKB analysis of the generalized hypergeometric differential equation, I
(RIMS Symposium (Open) "Various Problems of Algebraic Analysis" 2018)
Exact WKB analysis of the hypergeometric differential equation
(Differential equations in the complex domain and related topics 2018)
Exact WKB analysis of the Gauss hypergeometric function
(Microlocal Analysis and Asymptotic Analysis 2017)

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Education (4)：

- 1981 The University of Tokyo
- 1981 The University of Tokyo Graduate School, Division of Science
- 1976 The University of Tokyo Faculty of Science
- 1976 The University of Tokyo Faculty of Science

Professional career (2)：

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Association Membership(s) (1)：

日本数学会

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