Faculty Profiles - TAIRA KOUICHI

Information

写真a

TAIRA KOUICHI

Organization

Faculty of Mathematics Division of Analysis Associate Professor
School of Sciences Department of Mathematics（Concurrent）
Graduate School of Mathematics Department of Mathematics（Concurrent）
Joint Graduate School of Mathematics for Innovation （Concurrent）

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

https://sites.google.com/view/the-home-page-of-kouichi-taira/home
Personal 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

researchmap
Ritsumeikan University College of Science and Engineering Assistant Professor

2021.4 - 2024.3

　 More details

researchmap
立命館大学，助教，2021年4月-2024年3月

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

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
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
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
Uniform resolvent estimates for the discrete Schrödinger operator in dimension three

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

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 onL^p-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

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

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

372 ( 7 ) 5243 - 5262 2019.6

　More details

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

DOI： 10.1090/tran/7882

▼display all

Professional Memberships

日本数学会
日本数学会

　 More details

researchmap

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

日本学術振興会科学研究費助成事業若手研究

　 More details

Authorship：Principal investigator Grant type：Scientific research funding

Class subject

数学展望II

2024.4 - 2024.9 First semester

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

Travel Abroad

2019.10 - 2019.11

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