Updated on 2022/10/26

写真a

 
Kaizuka Koichi
 
Affiliation
Faculty of Medicine, Department of Mathematics, Senior Assistant Professor
Title
Senior Assistant Professor
External link

Degree

  • 博士(理学) ( 東北大学 )

Research Interests

  • 対称空間

  • スペクトル理論

  • 調和解析

Research Areas

  • Natural Science / Basic analysis

Research History

  • Nippon Medical School   Medical School   Senior Assistant Professor

    2017.4

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  • Gakushuin University   Faculty of Science   Assistant Professor

    2014.9 - 2017.3

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  • Ritsumeikan University   Research Organization of Science and Technology

    2014.4 - 2014.8

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  • Nippon Medical School   Senior Assistant Professor

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Professional Memberships

Papers

  • Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application to a conjecture of Strichartz Reviewed

    Koichi KAIZUKA

    J. Funct. Anal.   276 ( 2 )   329 - 379   2019

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

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  • A characterization of the L^2-range of the Poisson transform with real and singular spectral parameter on symmetric spaces of noncompact type Reviewed

    Koichi KAIZUKA

    J. Lie Theory   28 ( 2 )   581 - 607   2018

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

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  • A characterization of the L-2-range of the Poisson transform related to Strichartz conjecture on symmetric spaces of noncompact type Reviewed

    Koichi Kaizuka

    ADVANCES IN MATHEMATICS   303   464 - 501   2016.11

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    The main purpose of this paper is to solve Strichartz conjecture concerning an image characterization of the Poisson transform in the L-2-theory on symmetric spaces of noncom pact type. We prove that the Poisson transform provides an isomorphism between the L-2-space on the boundary and a certain weighted L-2-space consisting of joint eigenfunctions on symmetric spaces of noncompact type. Our approach is based on the scattering theory for the Schrodinger operator. Moreover, we give a Fourier restriction estimate and an asymptotic formula for the Poisson transform. (C) 2016 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.aim.2016.08.020

    Web of Science

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  • Resolvent estimates on symmetric spaces of noncompact type Reviewed

    Koichi Kaizuka

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   66 ( 3 )   895 - 926   2014.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：MATH SOC JAPAN  

    In this article we prove resolvent estimates for the Laplace-Beltrami operator or more general elliptic Fourier multipliers on symmetric spaces of noncompact type. Then the Kato theory implies time-global smoothing estimates for corresponding dispersive equations, especially the Schrodinger evolution equation. For low-frequency estimates, a pseudo-dimension appears as an upper bound of the order of elliptic Fourier multipliers. A key of the proof is to show a weighted L-2-continuity of the modified Radon transform and fractional integral operators.

    DOI： 10.2969/jmsj/06630895

    Web of Science

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Misc.

  • 書評「谷島賢二：シュレディンガー方程式 I, II (朝倉数学体系 5, 6)」 Invited Reviewed

    貝塚 公一

    日本数学会「数学」   70 ( 1 )   101 - 106   2018.1

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  • A characterization of the L^2-range of the Poisson transform with real and singular spectral parameter on symmetric spaces of noncompact type Invited

    貝塚 公一

    数理解析研究所講究禄「スペクトル・散乱理論とその周辺」   2045   100 - 116   2017.10

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Presentations

  • A characterization of the L^2-range of the Poisson transform with real and singular spectral parameter on symmetric spaces of noncompact type Invited

    貝塚 公一

    第149回神楽坂解析セミナー, 東京理科大学  2017.6 

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  • A characterization of the L^2-range of the Poisson transform with real and singular spectral parameter on symmetric spaces Invited

    貝塚 公一

    研究集会「微分方程式と幾何学」, 立命館大学  2017.6 

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  • A characterization of the L^2-range of the Poisson transform with real and singular spectral parameter on symmetric spaces of noncompact type Invited

    貝塚 公一

    研究集会「The 15th Linear and Nonlinear waves」  2017.11 

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  • Scattering theory for the Laplacian on symmetric spaces of noncompact type Invited

    貝塚 公一

    数理科学科談話会, 立命館大学  2014.6 

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  • Scattering theory for the Laplacian on symmetric spaces of noncompact type Invited

    貝塚 公一

    微分方程式セミナー, 大阪大学  2014.7 

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  • Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application Invited

    貝塚 公一

    作用素論セミナー, 京都大学数理解析研究所  2014.6 

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    Venue：岡山大学  

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  • Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application Invited

    貝塚 公一

    第53回 実函数論・函数解析学合同シンポジウム, 学習院大学  2014.9 

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  • Scattering theory for the Laplacian on symmetric spaces of noncompact type Invited

    貝塚 公一

    第61回 幾何学シンポジウム, 名城大学  2014.8 

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  • Scattering theory for the Laplacian on symmetric spaces of noncompact type Invited

    貝塚 公一

    微分方程式セミナー, 名古屋大学  2014.12 

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  • Scattering theory for the Laplacian on symmetric spaces of noncompact type Invited

    貝塚 公一

    理学部数学科談話会, 学習院大学  2014.11 

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  • Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application Invited

    Koichi KAIZUKA

    Analysis and Geometry Seminar, Northeastern University, U.S.A.  2015.3 

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  • Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application Invited

    貝塚 公一

    調和解析駒場セミナー, 東京大学大学院数理科学研究科  2015.1 

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  • Asymptotic properties of solutions of the Helmholtz equation on symmetric spaces of noncompact type Invited

    Koichi KAIZUKA

    MIT Lie groups Seminar, Massachusetts Institute of Technology, U.S.A.  2015.3 

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  • Stationary scattering theory on symmetric spaces Invited

    貝塚 公一

    RIMS合宿型セミナー「Workshop on linear and nonlinear dispersive equations and related topics」  2017.5 

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  • Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application Invited

    貝塚 公一

    Rigidity Seminar, 名古屋大学  2014.5 

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  • Stationary scattering theory for invariant differential operators on symmetric spaces of noncompact type Invited

    貝塚 公一

    日本数学会2017年度春季総合分科会, 函数解析学分科会特別公演  2017.3 

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    Presentation type：Oral presentation (invited, special)  

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Research Projects

  • 対称空間上のディラック作用素に対するスペクトル解析

    2017.4 - 2019.3

    学術研究助成基金助成金  若手研究（B） 

    貝塚 公一

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    Authorship：Principal investigator  Grant type：Competitive

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Teaching Experience

  • 微分方程式入門演習

    Institution：学習院大学

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  • 微分積分 I 演習

    Institution：学習院大学

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  • ルベーグ積分演習

    Institution：学習院大学

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  • 自然科学の数学的基礎

    Institution：日本医科大学

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  • 数学輪講２

    Institution：学習院大学

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  • 数学１化１年

    Institution：学習院大学

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  • 線形代数

    Institution：日本医科大学

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  • 数学輪講１

    Institution：学習院大学

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  • 数学２化１年

    Institution：学習院大学

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  • 微分積分 II 演習

    Institution：学習院大学

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