Updated on 2025/06/11

Information

 

写真a

 
TAIRA KOUICHI
 
Organization
Faculty of Mathematics Division of Analysis Associate Professor
Joint Graduate School of Mathematics for Innovation （Concurrent）
School of Sciences Department of Mathematics（Concurrent）
Graduate School of Mathematics Department of Mathematics（Concurrent）
Title
Associate Professor
Profile
微分作用素，Schrödinger作用素のスペクトル理論について超局所解析，調和解析の手法を用いて研究しています．Schrödinger作用素は量子力学系のエネルギーに対応するものですが，超局所解析を用いて解析することにより古典力学系との対応関係のもとでそのスペクトルの性質を調べることができます．特に興味があるのはLorentz多様体上のスペクトル理論です．このトピックに関して近年では表現論の分野で興味深い進展があった他，曲がった時空上の場の量子論への応用も指摘されています．一方で既存の道具が使えない場面が多々現れるので，自ら手法を開拓していく必要があり，それも面白さの一つです．他にも，時間依存Schrödinger方程式の平滑化効果にも関心があります．
Homepage
External link

Research Areas

  • Natural Science / Mathematical analysis

Degree

  • 学士（理学）（東京大学，日本）

  • Master degree (Mathematical Science) (The university of Tokyo, Japan)

  • Ph.D.(Mathematical Science) (The university of Tokyo, Japan)

Research History

  • Kyushu University Faculty of Mathematics Associate Professor 

    2024.4 - Present

    　 More details

  • Ritsumeikan University College of Science and Engineering Assistant Professor 

    2021.4 - 2024.3

    　 More details

  • 立命館大学，助教，2021年4月-2024年3月   

Education

  • The University of Tokyo   Graduate School of Mathematical Sciences  

    2017.4 - 2020.3

    　 More details

    Country：Japan

  • The University of Tokyo   Graduate School of Mathematical Sciences  

    2015.4 - 2017.3

    　 More details

    Country：Japan

Research Interests・Research Keywords

  • Research theme： Spectral theory of differential operators, Smoothing effects for Schrödinger equations

    Keyword： Schrödinger equations, Spectrum, Microlocal analysis

    Research period： 2024.4

  • Research theme： 超局所解析

    Keyword： 超局所解析

    Research period： 2024

  • Research theme： 散乱理論

    Keyword： 散乱理論

    Research period： 2024

  • Research theme： スペクトル理論

    Keyword： スペクトル理論

    Research period： 2024

  • Research theme： シュレディンガー方程式

    Keyword： シュレディンガー方程式

    Research period： 2024

Papers

  • Local Time Decay for Fractional Schrödinger Operators with Slowly Decaying Potentials

    Kouichi Taira

    Annales Henri Poincaré   2025.3   （ ISSN:1424-0637 eISSN:1424-0661 ）

    　More details

    Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    A local time decay estimate of fractional Schrödinger operators with slowly decaying positive potentials is studied. It is shown that the resolvent is smooth near zero, and the time propagator exhibits fast local time decay, which is very different from very short-range cases. The key element of the proof is to establish a weaker Agmon estimate for a classically forbidden region using exotic symbol calculus. As a byproduct, we prove that the Riesz operator is a pseudodifferential operator with an exotic symbol.

    DOI： 10.1007/s00023-025-01560-4

    Web of Science

    Scopus

    researchmap

    Other Link： https://link.springer.com/article/10.1007/s00023-025-01560-4/fulltext.html

  • Strichartz Estimates for the $(k,a)$-Generalized Laguerre Operators

    Kouichi Taira, Hiroyoshi Tamori

    Symmetry, Integrability and Geometry: Methods and Applications   21   2025   （ ISSN:1815-0659 eISSN:1815-0659 ）

    　More details

    Publishing type：Research paper (scientific journal)   Publisher：SIGMA (Symmetry, Integrability and Geometry: Methods and Application)  

    In this paper, we prove Strichartz estimates for the $(k,a)$-generalized Laguerre operators $a^{-1}\bigl(-|x|^{2-a}\Delta_k+|x|^a\bigr)$ which were introduced by Ben Saïd-Kobayashi-Ørsted, and for the operators $|x|^{2-a}\Delta_k$. Here $k$ denotes a non-negative multiplicity function for the Dunkl Laplacian $\Delta_k$ and $a$ denotes a positive real number satisfying certain conditions. The cases $a=1,2$ were studied previously. We consider more general cases here. The proof depends on symbol-type estimates of special functions and a discrete analog of the stationary phase theorem inspired by the work of Ionescu-Jerison.

    DOI： 10.3842/SIGMA.2025.014

    Web of Science

    Scopus

    researchmap

  • Smoothness of the fundamental solution of Schrödinger equations with mild trapping

    Kouichi Taira

    Proc. Amer. Math. Soc.   151   2073 - 2080   2023.2

    　More details

    Language：Others   Publisher：American Mathematical Society (AMS)  

    DOI： 10.1090/proc/16271

    researchmap

  • A Remark on the Essential Self-adjointness for Klein–Gordon-Type Operators

    Shu Nakamura, Kouichi Taira

    Annales Henri Poincaré   2023.2   （ ISSN:1424-0637 eISSN:1424-0661 ）

    　More details

    Language：Others   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    DOI： 10.1007/s00023-023-01277-2

    researchmap

    Other Link： https://link.springer.com/article/10.1007/s00023-023-01277-2/fulltext.html

  • Essential Self-Adjointness of Klein-Gordon Type Operators on Asymptotically Static, Cauchy-Compact Spacetimes

    Shu Nakamura, Kouichi Taira

    Communications in Mathematical Physics   398 ( 3 )   1153 - 1169   2022.11   （ ISSN:0010-3616 eISSN:1432-0916 ）

    　More details

    Language：Others   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    DOI： 10.1007/s00220-022-04543-2

    researchmap

    Other Link： https://link.springer.com/article/10.1007/s00220-022-04543-2/fulltext.html

  • A remark on Strichartz estimates for Schrödinger equations with slowly decaying potentials

    Kouichi Taira

    Proceedings of the American Mathematical Society   150 ( 9 )   3953 - 3958   2022.4   （ ISSN:0002-9939 eISSN:1088-6826 ）

    　More details

    Language：Others   Publishing type：Research paper (scientific journal)   Publisher：American Mathematical Society (AMS)  

    <p>In this short note, we prove Strichartz estimates for Schrödinger operators with slowly decaying singular potentials in dimension two. This is a generalization of the recent results by Mizutani, which are stated for dimension greater than two. The main ingredient of the proof is a variant of Kato’s smoothing estimate with a singular weight.</p>

    DOI： 10.1090/proc/15954

    researchmap

  • Remarks on the geodesically completeness and the smoothing effect on asymptotically Minkowski spacetimes

    Kouichi Taira

    Letters in Mathematical Physics   112 ( 2 )   2022.4   （ ISSN:0377-9017 eISSN:1573-0530 ）

    　More details

    Language：Others   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    DOI： 10.1007/s11005-022-01517-2

    researchmap

    Other Link： https://link.springer.com/article/10.1007/s11005-022-01517-2/fulltext.html

  • Uniform resolvent estimates for the discrete Schrödinger operator in dimension three

    Kouichi Taira

    Journal of Spectral Theory   11 ( 4 )   1831 - 1855   2021.12

    　More details

    Language：Others   Publishing type：Research paper (scientific journal)  

    DOI： 10.4171/jst/387

  • Limiting Absorption Principle and Equivalence of Feynman Propagators on Asymptotically Minkowski Spacetimes

    Kouichi Taira

    Communications in Mathematical Physics   388 ( 1 )   625 - 655   2021.11

    　More details

    Language：Others   Publishing type：Research paper (scientific journal)  

    DOI： 10.1007/s00220-021-04196-7

  • Scattering theory for repulsive Schrödingeroperators and applications to the limit circle problem

    Kouichi Taira

    Analysis & PDE   14 ( 7 )   2101 - 2122   2021.11

    　More details

    Language：Others   Publishing type：Research paper (scientific journal)  

    DOI： 10.2140/apde.2021.14.2101

  • Essential self-adjointness of real principal type operators

    Shu Nakamura, Kouichi Taira

    Annales Henri Lebesgue   4   1035 - 1059   2021.9

    　More details

    Language：Others   Publishing type：Research paper (scientific journal)  

    DOI： 10.5802/ahl.96

  • Limiting absorption principle onLp-spaces and scattering theory

    Kouichi Taira

    Journal of Mathematical Physics   61 ( 9 )   092106 - 092106   2020.9

    　More details

    Language：Others   Publishing type：Research paper (scientific journal)  

    DOI： 10.1063/5.0011805

  • Some Properties of Threshold Eigenstates and Resonant States of Discrete Schrödinger Operators

    Yuji Nomura, Kouichi Taira

    Annales Henri Poincaré   21 ( 6 )   2009 - 2030   2020.6

    　More details

    Language：Others   Publishing type：Research paper (scientific journal)  

    DOI： 10.1007/s00023-020-00912-6

  • Strichartz estimates for non‐degenerate Schrödinger equations

    Kouichi Taira

    Mathematische Nachrichten   293 ( 4 )   774 - 793   2020.4

    　More details

    Language：Others   Publishing type：Research paper (scientific journal)  

    DOI： 10.1002/mana.201800148

  • Uniform bounds of discrete Birman–Schwinger operators

    Yukihide Tadano, Kouichi Taira

    Transactions of the American Mathematical Society   372 ( 7 )   5243 - 5262   2019.6

    　More details

    Language：Others   Publishing type：Research paper (scientific journal)  

    DOI： 10.1090/tran/7882

▼display all

Presentations

  • The WKB method and its application to spectral theory Invited

    Kouichi Taira

    Lectures on Semi-Classical Analysis  2024.10 

    　More details

    Event date： 2024.10

    Language：English   Presentation type：Oral presentation (general)  

    Venue：Ritsumeikan University  

Professional Memberships

Academic Activities

  • Screening of academic papers

    Role(s)： Peer review

    2024

    　More details

    Type：Peer review 

    Number of peer-reviewed articles in foreign language journals：2

    Number of peer-reviewed articles in Japanese journals：0

    Proceedings of International Conference Number of peer-reviewed papers：0

    Proceedings of domestic conference Number of peer-reviewed papers：0

  • Screening of academic papers

    Role(s)： Peer review

    2023

    　More details

    Type：Peer review 

    Number of peer-reviewed articles in foreign language journals：5

  • Screening of academic papers

    Role(s)： Peer review

    2021

    　More details

    Type：Peer review 

    Number of peer-reviewed articles in foreign language journals：3

Research Projects

  • シュレディンガー作用素のスペクトル理論

    Grant number：23K13004  2023 - 2027

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Early-Career Scientists

    　 More details

    Authorship：Principal investigator  Grant type：Scientific research funding

Class subject

  • 数学展望II

    2024.4 - 2024.9   First semester

  • Advanced Infinite Analysis

    2025.10 - 2026.3   Second semester

  • 無限解析

    2025.10 - 2026.3   Second semester

  • 数学概論Ⅲ・演習

    2025.10 - 2026.3   Second semester

  • 微分積分学Ⅱ

    2025.10 - 2026.3   Second semester

  • 入門線形代数Ⅱ

    2025.6 - 2025.8   Summer quarter

  • 解析学Ⅰ・演習

    2025.4 - 2025.9   First semester

  • 数理科学特論１１

    2025.4 - 2025.9   First semester

  • 数理科学特別講義Ⅺ

    2025.4 - 2025.9   First semester

  • 微分積分学Ⅰ

    2025.4 - 2025.9   First semester

  • Special Lectures Ⅺ

    2025.4 - 2025.9   First semester

  • 入門線形代数Ⅰ

    2025.4 - 2025.6   Spring quarter

▼display all

FD Participation

  • 2024.4   Role：Participation   Title：令和６年度第１回全学FD（新任教員研修）

    Organizer：University-wide

  • 2024.4   Role：Participation   Title：令和６年度 第１回全学FD（新任教員の研修）The 1st All-University FD (training for new faculty members) in FY2024

    Organizer：University-wide

Travel Abroad

  • 2019.10 - 2019.11

    Staying countory name 1：France   Staying institution name 1：Paris-Saclay University