Organization
Graduate School of Mathematics Division of Mathematics Fundamental Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science
Title
Professor
SUGIMOTO Mitsuru
Degree 1
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博士（理学） （ 1992.2 ）
Research Areas 1
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Others / Others / Basic Analysis
Current Research Project and SDGs 3
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フーリエ積分作用素の有界性とその応用
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発展方程式の時空間評価
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関数空間論
Professional Memberships 2
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日本数学会
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アメリカ数学会
Committee Memberships 9
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日本数学会 理事
2018.4 - 2024.5
Committee type：Academic society
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日本数学会函数方程式論分科会 連絡責任評議員
2017.4 - 2020.3
Committee type：Academic society
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日本数学会Journal 編集委員会 編集委員
2016.7 - 2022.6
Committee type：Academic society
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日本数学会学術委員会 運営委員
2013.7 - 2019.6
Committee type：Academic society
委員長 2017年7月1日～継続中
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日本数学会学術委員会 委員長
2017.7 - 2019.6
Committee type：Academic society
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日本数学会教育資金問題検討委員会 運営委員
2014.7 - 2018.6
Committee type：Academic society
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日本数学会ニュースレター委員会 委員
2013.7 - 2016.6
Committee type：Academic society
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Board
2010
Committee type：Academic society
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京都大学数理解析研究所 専門委員
2021.9 - 2023.8
Awards 2
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The MSJ Analysis Prize
2015.9 The Mathematical Society of Japan
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Daiwa Adrian Prize
2010.12 The Daiwa Anglo-Japanese Foundation
Papers 32
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Scaling limit of modulation spaces and their applications Reviewed International coauthorship
Sugimoto Mitsuru, Wang Baoxiang
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS Vol. 53 page： 54 - 94 2021.7
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Nonlinear operations on a class of modulation spaces Reviewed
Kato Tomoya, Sugimoto Mitsuru, Tomita Naohito
JOURNAL OF FUNCTIONAL ANALYSIS Vol. 278 ( 9 ) 2020.5
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A local-to-global boundedness argument and Fourier integral operators Reviewed
Ruzhansky Michael, Sugimoto Mitsuru
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Vol. 473 ( 2 ) page： 892 - 904 2019.5
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Remarks on the Mizohata-Takeuchi conjecture and related problems
Bez Neal, Sugimoto Mitsuru
ASYMPTOTIC ANALYSIS FOR NONLINEAR DISPERSIVE AND WAVE EQUATIONS Vol. 81 page： 1 - 12 2019
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Stability of Trace Theorems on the Sphere Reviewed
Bez Neal, Jeavons Chris, Ozawa Tohru, Sugimoto Mitsuru
JOURNAL OF GEOMETRIC ANALYSIS Vol. 28 ( 2 ) page： 1456 - 1476 2018.4
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OPTIMAL CONSTANTS AND EXTREMISERS FOR SOME SMOOTHING ESTIMATES Reviewed
Bez Neal, Sugimoto Mitsuru
JOURNAL D ANALYSE MATHEMATIQUE Vol. 131 page： 159 - 187 2017.3
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Extremisers for the trace theorem on the sphere Reviewed
Neal Bez, Shuji Machihara, Mitsuru Sugimoto
Math. Res. Lett. Vol. 23 page： 633-647 2016
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Smoothing estimates for non-dispersive equations Reviewed
Michael Ruzhansky, Mitsuru Sugimoto
Math. Ann. Vol. 365 page： 241-269 2016
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Local well-posedness for the Davey -Stewartson equation in generalized Feichtinger algebra Reviewed
Mitsuru Sugimoto, Baoxiang Wang, Rongrong Zhang
J. Fourier Anal. Appl. Vol. 21 page： 1105-1129 2015
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Trace theorems: critical cases and best constants Reviewed
Michael Ruzhansky, Mitsuru Sugimoto
Proc. Amer. Math. Soc. Vol. 143 page： 227-237 2015
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Applications of the Funk-Hecke theorem to smoothing and trace estimates Reviewed
Neal Bez, Hiroki Saito, Mitsuru Sugimoto
Adv. Math. Vol. 285 page： 1767-1795 2015
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Optimal forward and reverse estimates of Morawetz and Kato-Yajima type with angular smoothing index Reviewed
Neal Bez, Mitsuru Sugimoto
J. Fourier Anal. Appl. Vol. 21 page： 318-341 2015
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On global inversion of homogeneous maps Reviewed
Michael Ruzhansky, Mitsuru Sugimoto
Bull. Math. Sci. Vol. 5 page： 13-18 2015
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Inclusion relations between Lp-Sobolev and Wiener amalgam spaces Reviewed
Jayson Cunanan, Masaharu Kobayashi, Mitsuru Sugimoto
J. Funct. Anal. Vol. 268 page： 239-254 2015
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Unimodular Fourier multipliers on Wiener amalgam spaces Reviewed
Jayson Cunanan, Mitsuru Sugimoto
Vol. 419 page： 738-747 2014
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Smoothing properties of evolution equations via canonical transforms and comparison principle Reviewed
Michael Ruzhansky, Mitsuru Sugimoto
Proc. London Math. Soc. Vol. 105 page： 393-423 2012
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Structural resolvent estimates and derivative nonlinear Schrödinger equations Reviewed
Michael Ruzhansky, Mitsuru Sugimoto
Comm. Math. Phys. Vol. 314 page： 281-304 2012
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The inclusion relation between Sobolev and modulation spaces Reviewed
Masaharu. Kobayashi, Mitsuru Sugimoto
J. Funct. Anal. Vol. 260 page： 3189-3208 2011
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Remarks on nonlinear operations on modulation spaces Reviewed
Mitsuru Sugimoto, Naohito Tomita, Baoxiang Wang
Integral Transforms and Spec. Funct. Vol. 22 page： 351-358 2011
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Changes of variables in modulation and Wiener amalgam spaces Reviewed
Michael Ruzhansky, Mitsuru Sugimoto, Joachim Toft, Naohito Tomita
Math. Nachr. Vol. 284 page： 2078 - 2092 2011
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Weighted Sobolev L2 estimates for a class of Fourier integral operators Reviewed
Michael Ruzhansky, Mitsuru Sugimoto
Math. Nachr. Vol. 284 page： 1715-1738 2011
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Motion of elastic wire with thickness Reviewed
Norihito Koiso, Mitsuru Sugimoto
Osaka J. Math. Vol. 47 page： 787–815 2010
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Criteria for Bochner's extension problem Reviewed
Michael Ruzhansky, Mitsuru Sugimoto
Asymptot. Anal. Vol. 66 page： 125–138 2010
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*Trace ideals for pseudo-differential operators and their commutators with symbols in α-modulation spaces Reviewed
Masaharu. Kobayashi, Mitsuru Sugimoto, Naohito Tomita
J. Anal. Math. Vol. 107 page： 141-160 2009
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On the L2-boundedness of pseudo-differential operators and their commutators with symbols in α-modulation spaces Reviewed
Masaharu. Kobayashi, Mitsuru Sugimoto, Naohito Tomita
J. Math. Anal. Appl. Vol. 350 page： 157-169 2009
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A remark on fractional integrals on modulation spaces Reviewed
Mitsuru Sugimoto, Naohito Tomita
Math. Nachr. Vol. 281 page： 1372–1379 2008
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Boundedness properties of pseudo-differential and Calderon-Zygmund operators on modulation spaces Reviewed
Mitsuru Sugimoto, Naohito Tomita
J. Fourier Anal. Appl. Vol. 14 page： 124-143 2008
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A counterexample for boundedness of pseudo-differential operators on modulation spaces Reviewed
Mitsuru Sugimoto, Naohito Tomita
Proc. Amer. Math. Soc. Vol. 136 page： 1681-1690 2008
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*The dilation property of modulation spaces and their inclusion relation with Besov spaces Reviewed
Mitsuru Sugimoto, Naohito Tomita
J. Funct. Anal. Vol. 248 page： 79-106 2007
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*Global L2-boundedness theorems for a class of Fourier integral operators Reviewed
Michael Ruzhansky, Mitsuru Sugimoto
Comm. Partial Differential Equations Vol. 31 page： 547-569 2006
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*A smoothing property of Schrodinger equations in the critical case Reviewed
Michael Ruzhansky, Mitsuru Sugimoto
Math. Ann. Vol. 335 page： 645-673 2006
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*A Smoothing property of Schrodinger equations along the sphere Reviewed
Mitsuru Sugimoto
J. Anal. Math. Vol. 89 page： 15-30 2003
Books 4
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フーリエ解析入門
エリアス・Ｍ．スタイン，ラミ・シャカルチ著 新井仁之，杉本 充，高木啓行，千原浩之訳（ Role： Joint author）
日本評論社 2007.3
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複素解析
エリアス・Ｍ．スタイン，ラミ・シャカルチ著新井仁之，杉本 充，高木啓行，千原浩之訳（ Role： Joint author）
日本評論社 2009.6
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実解析
エリアス・Ｍ．スタイン，ラミ・シャカルチ著 新井仁之，杉本 充，高木啓行，千原浩之訳 （ Role： Joint translator）
日本評論社 2017.12
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関数解析 より進んだ話題への入門
エリアス・Ｍ．スタイン，ラミ・シャカルチ著 新井仁之，杉本 充，高木啓行，千原浩之訳 （ Role： Joint translator）
日本評論社 2024.9
Presentations 95
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On a global inverse function theorem for homogeneous maps Invited International coauthorship International conference
杉本充
Linear and Nonlinear Waves, No.20 2023.11.23 大阪大学理学研究科
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制限定理と関連する偏微分方程式論の諸問題 Invited
杉本充
談話会 2023.6.28 京都大学大学院理学研究科
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A constructive approach to nonlinear wave equations Invited International conference
2022.8.24
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A constructive approach to nonlinear wave equations Invited International conference
2022.5.19 Ghent Analysis & PDE Centre
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A constructive approach to nonlinear wave equations Invited
Mitsuru Sugimoto
2022.4.11
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A constructive approach to nonlinear damped wave equations Invited International conference
2021.8.4
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A constructive approach to semilinear wave equations Invited International conference
Mitsuru Sugimoto
Asia-Pacific Analysis and PDE semina 2021.1.25
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非線形波動方程式の自己相似解の構成法について Invited
杉本 充
分散型方程式と実解析 2020.12.9 大阪大学
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On a construction of self-similar solutions to nonlinear wave equations Invited
Mitsuru Sugimoto
2020.9.3
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On a construction of self-similar solutions to nonlinear wave equations Invited
Mitsuru Sugimoto
2019.11.27
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On a construction of self-similar solutions to nonlinear wave equations Invited
Mitsuru Sugimoto
2019.11.22
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On self-similar solutions to nonlinear wave equations Invited International conference
Function Spaces and Geometric Analysis and Their Applications
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On construction of self-similar solutions to nonlinear wave equations Invited International conference
Anomalies in Partial Differential Equations
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A trial to construct specific self-similar solutions for nonlinear wave equations Invited International conference
The 12th ISAAC Congress
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Optimal trace theorems on the sphere and their stability Invited International conference
The 8th SEAMS-UGM International Conference on Mathematics and Its Applications
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A specific construction of self-similar solutions for nonlinear wave equations Invited
Regularity and Asymptotic Analysis for Critical Phenomena of Partial Differential Equations
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Optimal trace theorems on the sphere Invited International conference
The Legacy of Joseph Fourier after 250 years
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Spectral identities and the comparison principle of smoothing estimates for evolution equations Invited International conference
Partial Differential Equation and General Relativity
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Spectral identities and the comparison principle of smoothing estimates Invited International conference
Mitsuru Sugimoto
Al-Khorezmiy 2018
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Remarks on nonlinear operations on modulation spaces Invited
Mitsuru Sugimoto
Harmonic analysis and the Navier-Stokes equations
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Spectral identities and smoothing estimates for evolution operators Invited
Mitsuru Sugimoto
Seminar
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Optimal estimates of Kato-Yajima type with angular smoothing Invited
Mitsuru Sugimoto
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A local-to-global boundedness argument and Fourier integral operators Invited International conference
Mitsuru Sugimoto
Hyperbolic Partial Differ- ential Equations and Related Topics
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制限定理と関連する偏微分方程式論の諸問題 Invited
杉本充
談話会
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Spectral comparison of smoothing estimates Invited
Mitsuru Sugimoto
Recent Topics on Partial Differential Equations
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Spectral Comparison of Smoothing Estimates Invited International conference
Mitsuru Sugimoto
The 11th ISAAC Congress
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Remarks on nonlinear operations on modulation spaces Invited
Mitsuru Sugimoto
Harmonic Analysis and its Applications in Tokyo 2017
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制限定理と関連する偏微分方程式論の諸問題 Invited
杉本充
談話会
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Spectral comparison of smoothing estimates and its applications Invited International conference
Mitsuru Sugimoto
8th International conference on Mathematical Modeling
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Remarks on nonlinear operations on modulation spaces Invited International conference
Mitsuru Sugimoto
Aspects of Time-Frequency Analysis
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Spectral comparison of smoothing estimates and its applications Invited
Mitsuru Sugimoto
Critical Exponents and Nonlinear Evolution Equation 2017
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Optimal smoothing estimates and trace theorems Invited
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Optimal smoothing estimates and a related PDE problem Invited International conference
Mitsuru Sugimoto
Modern problems of applied mathematics and information technologies - Al-Khorezmiy 2016 -
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Optimal smoothing estimates and related topics Invited
Mitsuru Sugimoto
Linear and Nonlinear Waves, No.14
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平滑化評価式および制限定理の最良定数と関連する話題 Invited
杉本 充
第55回実函数論・関数解析学合同シンポジウム
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Optimal trace theorems and a related PDE problem International conference
Mitsuru Sugimoto
Fourier Analysis and Applications Workshop
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Smoothing estimates for non-dispersive equations Invited
Mitsuru Sugimoto
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A criterion for the global boundedness of locally bounded integral operators Invited International conference
Mitsuru Sugimoto
4th East Asian Conference in Harmonic Analysis and Applications
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Optimal trace theorems and their relation to a PDE problem Invited
Mitsuru Sugimoto
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Optimal smoothing estimates and trace theorems
Mitsuru Sugimoto
Coloquium
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シュレディンガー方程式の角方向への平滑化作用について Invited
杉本 充
日本数学会２０１６年度年会 2015年度第14回解析学賞受賞特別講演
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Optimal smoothing estimates and trace theorems Invited
Mitsuru Sugimoto
Harmonic Analysis, Geometric Analysis and PDE workshop
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Optimal smoothing estimates Invited
Mitsuru Sugimoto
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Smoothing estimates for dispersive equations and related topics Invited
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On a condition for the global L^p-boundedness of Fourier integral operators Invited International conference
Mitsuru Sugimoto
Harmonic Analysis and its Applications in Tokyo 2015
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Optimal smoothing estimates Invited International conference
Mitsuru Sugimoto
Pure Analysis and PDEs seminar
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Global regularity properties of Fourier integral operators International conference
Mitsuru Sugimoto
The 10th ISAAC Congress
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平滑化評価式および制限定理の最良定数について
杉本 充
神楽坂解析セミナー
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分散型方程式における比較原理
杉本 充
第1回 解析学の耳袋
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On a systematic understanding of smoothing estimates for water wave equations International conference
Mitsuru Sugimoto
Seminar at Peking University
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A vector fields approach to smoothing and decaying estimates for equations in anisotropic media International conference
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On a systematic understanding of smoothing estimates for water wave equations International conference
Modern problems of applied mathematics and information technologies - Al-Khorezmiy 2014 -
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Smoothing estimates for third order equations in two spatial dimensions
Asymptotic Analysis of Nonlinear Dispersive and Wave Equations
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分散型方程式の比較原理に関する最近の話題
杉本充
第３回岐阜数理科学研究会
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Global regularity properties of Fourier integral operators International conference
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シュレディンガー方程式の平滑化評価式とスペクトル論的比較原理について
杉本充
応用解析研究会
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On a systematic understanding of smoothing estimates for water wave equations International conference
杉本充
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シュレディンガー方程式におけるスペクトル論的比較原理について
杉本充
南大阪応用数学セミナー
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分散型方程式の平滑化評価式に関する最近の進展
杉本充
日本数学会 函数方程式論分科会研究集会 ― 微分方程式の総合的研究 ―
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Optimal constants and extremisers for smoothing estimates of Kato-type
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A vector fields approach to smoothing and decaying estimates for equations in anisotropic media International conference
Mitsuru Sugimoto
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Optimal constants and extremisers for smoothing estimates of Kato-type International conference
Mitsuru Sugimoto
1st East Asian Conference in Harmonic analysis and Applications
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A vector fields approach to smoothing and decaying estimates for equations in anisotropic media International conference
Mitsuru Sugimoto
The 9th ISAAC Congres
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Recent progress in smoothing estimates for Schrödinger equations International conference
Mitsuru Sugimoto
Complex Analysis & Dynamical Systems VI
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Structural resolvent estimates and derivative nonlinear Schrodinger equations International conference
Mitsuru Sugimoto
Modern problems of applied mathematics and information technologies - Al-Khorezmiy 2012
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Optimal constants and extremisers for some smoothing estimates
Mitsuru Sugimoto
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Optimal constants and extremisers for some smoothing estimates International conference
Mitsuru Sugimoto
Phase space methods for pseudo-differential operators
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非等方的な媒質における方程式に対するベクトル場の方法によるアプローチ
杉本 充
広島微分方程式研究会
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平滑化評価式の最良定数について
杉本 充
第８回非線型の諸問題
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Optimal constants for some smoothing estimates International conference
Mitsuru Sugimoto
Fourier Analysis and Pseudo-Differential Operators
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平滑化評価式の最良定数について
杉本 充
名大微分方程式セミナー
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双曲型方程式初期値問題の解の減衰評価について
杉本 充
CREST流体数学講演会
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A vector fields approach to smoothing and decaying estimates for equations in anisotropic media International conference
Mitsuru Sugimoto
2011 NCTS Taiwan-Japan Joint Workshop on PDEs and Geometric Analysis
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フーリエ積分作用素を用いた偏微分方程式の定量的解析の試み
杉本 充
東北大学大学院理学研究科 談話会
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A vector fields approach to smoothing and decaying estimates for equations in anisotropic media
Mitsuru Sugimoto
The 4th MSJ-SI "NONLINEAR DYNAMICS IN PARTIAL DIFFERENTIAL EQUATIONS"
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Smoothing estimates for non-dispersive equations International conference
Mitsuru Sugimoto
The 8th ISAAC Congres
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The inclusion relation between Sobolev and modulation spaces International conference
Mitsuru Sugimoto
From Abstract to Computational Harmonic Analysis, Strobl 2011
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Elliptic Operators and Corresponding Vector Fields International conference
Mitsuru Sugimoto
Asymptotic Properties of Solutions to Hyperbolic Equations
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On some Lp-type estimates for evolution operators
Mitsuru Sugimoto
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On some Lp-type estimates for evolution operators International conference
Mitsuru Sugimoto
PDE Seminar
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Smoothing estimates for dispersive and non-dispersive equations International conference
Mitsuru Sugimoto
Analysis Seminar
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On some Lp-type estimates for evolution operators International conference
Mitsuru Sugimoto
Microlocal Day #2
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Smoothing estimates for dispersive and non-dispersive equations International conference
Mitsuru Sugimoto
2010 Workshop on Fourier Analysis and Its Applications to PDEs
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双曲型方程式の初期値問題における時間大域的な幾何光学解について
杉本 充
九州大学 関数方程式セミナー
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Optimal constants and extremisers for smoothing and trace estimates
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Smoothing estimates for dispersive and non-dispersive equations International conference
Mitsuru Sugimoto
International Conference on Generalized Functions GF2009
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Smoothing estimates for dispersive and non-dispersive equations International conference
Mitsuru Sugimoto
Nonlinear PDE in Zhang Jia Jie
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発展方程式に対する平滑化評価式について
杉本 充
第48回実函数論・関数解析学合同シンポジウム
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Space-time estimates for evolution equations via comparison International conference
Mitsuru Sugimoto
Harmonic Analysis and Partial Differential Equations with Applications
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分散型方程式の時空間評価式と比較原理
杉本 充
日本数学会2009年度年会 函数方程式論分科会
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Limiting absorption principle in the critical case and Sommerfeld radiation condition International conference
Mitsuru Sugimoto
PDEs and Function Spaces
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A limiting absorption principle in the critical case and a radiation condition International conference
Mitsuru Sugimoto
Decay and Regularity for Solutions of Differential Equations and Dynamical systems
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A limiting absorption principle in the critical case and a radiation condition International conference
Mitsuru Sugimoto
International Conference on Partial Differential Equations and Spectral Theory
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Smoothing estimates for dispersive equations via canonical transforms and comparison principle International conference
Mitsuru Sugimoto
Pseudo-differential Operators and Related Topics, II
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A constructive approach to nonlinear damped wave equations Invited International conference
MItsuru Sugimoto
The 13th ISAAC Congress 2021.8.4
KAKENHI (Grants-in-Aid for Scientific Research) 10
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Analysis of critical interactions in wave fields
Grant number：24H00024 2024.4 - 2029.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (S)
Authorship：Coinvestigator(s)
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Grant number：22K18673 2022.6 - 2025.3
科学研究費助成事業 挑戦的研究(萌芽)
杉本 充
Authorship：Principal investigator
Grant amount：\6370000 （ Direct Cost: \4900000 、 Indirect Cost：\1470000 ）
偏微分方程式において微分を多項式に対応させることにより得られるいわゆる表象は，対応する方程式の解に関する様々な情報の宝庫である．実際，偏微分方程式の解の特異性の位置などの定性的な情報を表象から抽出する方法論が，超局所解析の手法により既に確立されている．しかしながら解のなめらかさや大きさなど定量的な情報の抽出法については，依然としてその多くが未開拓のままである．この研究は，そのための様々な手法を模索しそれらを統合する形で，この眠れる鉱脈を掘り起こすための「定量的超局所解析」とでも言うべき一つの方法論を確立することを目指すものである．
この研究は，偏微分方程式における解のなめらかさや大きさなど定量的な性質の解析において，超局所解析の手法を取り込むための汎用性のある方法論を構築し，偏微分方程式論の研究における新しい可能性を追求していくものである．そのためには，偏微分方程式解のもつ構造のうちどの部分がその定量的性質に影響を与えているかを探ることがまずは重要と考えられるが，今年度は特に波動方程式に焦点をあて，その非線形問題の解を具体的に構成し今後の研究の方向性の指針とすることを試みた．これまでに冪型の非線形項をもつ波動方程式の初期値問題に対して，冪の指数がある範囲にとどまっていれば自己相似解が存在することが先行研究により示されていた．しかしながら，これらはあくまでも「存在証明」であり，自己相似解がどのような形をしているのかに関する知見までは得られていなかった．このような状況のもと今年度の研究成果により，超幾何函数を用いて具体的に自己相似解を構成するという新しい手段を得ることができた．さらに，この手法がスケール不変型の消散型波動方程式に対しても適用可能であることを見出し，これにより，時間大域解が存在するための臨界冪指数のシフト現象に対する新しい解釈を与えることが可能になった． また．これと並行して，多様体上などの一般的な状況における波動方程式の初期値問題の基本解に対する評価に関して，様々な知見が進むシュレデインガー方程式に対する評価式から導出する方法論の構築も試みた．
これまでの研究により，自己相似解が存在するための非線形項の冪の指数に対する条件は，超幾何関数の挙動から理解できるようになった．このように，非線形方程式の解の具体的な構造を見ることにより定量的性質をとらえることができた点は，今後の進展へと繋がる重要な成果と考えられる．
まずは，これまでに成果が上がっている自己相似解を具体的に構成する手法を，他の様々な方程式に対しても試みることにより，この方面での知見を拡げていきたい．同時に，波動方程式の Lp評価に関する課題に対しても重点的に取り組んで行きたい．具体的には，多様体上などの一般的な状況における波動方程式の初期値問題の基本解に対する Lｐ-評価に関して，既に様々な知見が得られているシュレデインガー方程式に対するLp-評価から導出する方法論の構築を試みたい．さらには分散型方程式の時空間評価において，局所的なものから大域的なものを導出する方法論を構築したい．これらはいずれも定量的な解析において超局所解析の手法を適用する典型例となることが期待される． -
Grant number：22H00098 2022.4 - 2027.3
科学研究費助成事業 基盤研究(A)
杉本 充, 高橋 太, BEZ NEAL
Authorship：Principal investigator
Grant amount：\38740000 （ Direct Cost: \29800000 、 Indirect Cost：\8940000 ）
本研究は，様々な函数不等式に対する最良定数と最良を達成する函数を決定する問題に対して，変分法・調和解析・表現論の手法を用いて多角的にアプローチし，偏微分方程式論も援用することによって，それらが定める基底状態としての諸相を突き止め，さらにはこれら異なる函数不等式の基底状態どうしの関連性にまで掘り下げて探究していくことにより，それらをより普遍的な法則として統一的に理解していくことを目指すものである．
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New perspectives on space-time estimates for dispersive equations
Grant number：19H01796 2019.4 - 2023.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
Bez Neal
Authorship：Coinvestigator(s)
A key outcome of this research project was the successful development of the theory of Strichartz estimates for orthonormal systems of initial data. In particular, significant progress has been made in the case of the wave equation, the Klein-Gordon equation, and the fractional Schrodinger equations. The first step was to establish certain oscillatory integral estimates with appropriate weights, and these estimates were combined with ideas of Frank-Sabin to obtain the Strichartz estimates for orthonormal initial data. Additionally, this research project initiated the study of Carleson's pointwise convergence problem for infinitely many fermions and significant progress was made in the one-dimensional case. This was achieved by first establishing orthonormal Strichartz estimates for fractional Schrodinger equations in a certain boundary case. It is expected that this paper will inspire further research in this direction.
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Comprehensive research of Einstein's equations based on analysis
Grant number：16H03940 2016.4 - 2021.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
Nakamura Makoto
Authorship：Coinvestigator(s)
Field equations with nonlinear terms representing various self-interactions were considered in homogeneous and isotropic spacetimes considered in cosmology, and the theory of the well-posedness for initial value problems (unique existence of solutions, asymptotic behaviors of solutions, and existence of blowing-up solutions) has been constructed. In the process, we constructed linear and nonlinear estimates for partial differential equations in homogeneous and isotropic spacetimes. Through this study, we characterized the effects of the expansion or contraction of spaces using the theory of partial differential equations, and their effects on behaviors of solutions of nonlinear partial differential equations.
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Quantitative analysis of PDE via method of microlocal analysis
Grant number：26287022 2014.4 - 2020.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
SUGIMOTO MITSURU
Authorship：Principal investigator
Grant amount：\15860000 （ Direct Cost: \12200000 、 Indirect Cost：\3660000 ）
For the analysis of quantitative properties (smoothness, size, etc.) of solutions to partial differential equations, a versatile method of utilizing the technique of microlocal analysis was constructed to pursue new possibility in the study of partial differential equations. The theory of Fourier integral operators as a tool to realize this idea, together with the theory of function spaces as its framework, were provided, and the effectiveness of this method was demonstrated by deriving various fundamental estimates for as general partial differential equations as possible, and by considering their properties.
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Phase space analysis by modulation spaces
Grant number：26610021 2014.4 - 2018.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research
SUGIMOTO Mitsuru, TOMITA NAOHITO, TERASAWA YUTAKA
Authorship：Principal investigator
Grant amount：\3510000 （ Direct Cost: \2700000 、 Indirect Cost：\810000 ）
We clarified the inclusion property between Wiener-amalgam spaces, which is defined in a similar way to modulation spaces, and Sobolev spaces. We also consider the application of modulation spaces to non-linear problems and discuss the local well-posedness of the Davey-Stewartson equation which describes a kind of water wave. In connection to it, we construct a theory of smoothing effect of non-dispersive equations. Furthermore, we gave an affirmative answer to the question “Does the composite function of a smooth function and a function in a modulation space belong to the same modulation space?”
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相空間解析における定量的な方法論の構築
2011.4 - 2014.3
科学研究費補助金 挑戦的萌芽研究、課題番号：23654049
杉本 充
Authorship：Principal investigator
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正準変換と比較原理の手法による分散型方程式の解の諸性質の解明
2008.4 - 2013.3
科学研究費補助金 基盤研究(B)
杉本 充
Authorship：Principal investigator
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偏微分方程式の定量的解析における新しい方法論
2008.4 - 2011.3
科学研究費補助金 萌芽研究，課題番号：20654015
杉本 充
Authorship：Principal investigator
Teaching Experience (On-campus) 27
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解析学要論III
2021
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現代数学基礎CII
2019
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複素関数論
2019
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解析学概論 Ⅳ
2018
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現代数学基礎CII
2018
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現代数学基礎AI
2017
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数学通論II
2016
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現代数学基礎AI
2016
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現代数学基礎AII
2015
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数学通論I
2015
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微分積分学 II
2014
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解析学I
2014
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微分積分学Ⅰ
2014
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解析学III
2013
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微分積分学 I
2013
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微分積分学 II
2013
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数学展望 II
2013
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Introduction to Concepts of Modern Mathematics
2011
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解析学要論Ⅲ
2010
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微分積分学Ⅱ
2010
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微分積分学Ⅰ
2010
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関数解析
2010
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解析学要論 III
2009
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微分積分学Ⅱ
2009
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微分積分学Ⅰ
2009
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微分積分学Ⅰ
2008
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微分積分学Ⅱ
2008
Teaching Experience (Off-campus) 6
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フーリエ積分作用素の理論とその応用
2008.4 - 2009.3 （Hokkaido University）
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フーリエ積分作用素の理論とその応用
2011.4 - 2012.3 （The University of Tokyo）
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フーリエ積分作用素の理論とその応用
2011.4 - 2012.3 （Tohoku University）
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フーリエ積分作用素の理論とその応用
2013.4 - 2014.3 （Osaka University）
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双曲型方程式とフーリエ解析
2015.4 - 2016.3 （Hokkaido University）
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分散型方程式の時空間評価式と調和解析の諸問題
2023.4 - 2024.3 （Kyoto University）
Level：Postgraduate Country：Japan
Social Contribution 2
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NHKカルチャー 数学散策
Role(s)：Lecturer
NHK文化センター 2016.5
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NHKカルチャー 数学逍遥
Role(s)：Lecturer
NHK文化センター 2015.10