Researcher Database

Masaharu Kobayashi
Faculty of Science Mathematics Mathematics
Associate Professor

Researcher Profile and Settings


  • Faculty of Science Mathematics Mathematics

Job Title

  • Associate Professor

J-Global ID

Research Interests

  • 関数空間   ウィナーアマルガム空間   モジュレーション空間   シュレディンガー方程式   実解析   直交級数   特異積分   ハーディー空間   調和解析   

Research Areas

  • Natural sciences / Basic analysis

Academic & Professional Experience

  • 2012 Tokyo University of Science

Association Memberships


Research Activities

Published Papers

  • Operating functions on modulation and Wiener amalgam spaces
    Masaharu Kobayashi, Enji Sato
    Nagoya Math. J. 230 72 - 82 2018 [Refereed][Not invited]
    Keiichi Kato, Masaharu Kobayashi, Shingo Ito
    OSAKA JOURNAL OF MATHEMATICS 54 (2) 209 - 228 0030-6126 2017/04 [Refereed][Not invited]
    In this paper, we give characterizations of usual wave front set and wave front set in H-s in terms of wave packet transform without any restriction on basic wave packet, which give complete answers of the question raised by G.B. Folland.
  • Estimates for Schrödinger operators on modulation spaces
    K.Kato, M.Kobayashi, S.Ito
    RIMS Kôkyûroku Bessatsu B60 129 - 143 2016 [Refereed][Not invited]
  • Jayson Cunanan, Masaharu Kobayashi, Mitsuru Sugimoto
    JOURNAL OF FUNCTIONAL ANALYSIS 268 (1) 239 - 254 0022-1236 2015/01 [Refereed][Not invited]
    We determined optimal inclusion relations between L-P-Sobolev and Wiener amalgam spaces. For applications, we discuss mapping properties of unimodular Fourier multipliers e(i vertical bar D vertical bar alpha) between L-P-Sobolev and Wiener amalgam spaces and derive some Littlewood-Paley type inequalities. (C) 2014 Elsevier Inc. All rights reserved.
  • Wave front set defined by wave packet transform and its application
    K.Kato, M.Kobayashi, S. Ito
    Adv. Stud. Pure Math., 64 417 - 425 2015 [Refereed][Not invited]
  • Keiichi Kato, Masaharu Kobayashi, Shingo Ito
    JOURNAL OF FUNCTIONAL ANALYSIS 266 (2) 733 - 753 0022-1236 2014/01 [Refereed][Not invited]
    In this paper we give new estimates for the solution to the Schrodinger equation with quadratic and sub-quadratic potentials in the framework of modulation spaces. (C) 2013 Published by Elsevier Inc.
  • Characterization of Wave Front Sets in Fourier-Lebesgue Spaces and Its Application
    Keiichi Kato, Masaharu Kobayashi, Shingo Ito
    FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA 56 (1) 1 - 17 0532-8721 2013/04 [Refereed][Not invited]
    In this paper, we characterize the Fourier-Lebesgue type wave front set by using the wave packet transform. We apply this to the propagation of singularities for the first order hyperbolic partial differential equations with constant coefficient.
  • Keiichi Kato, Masaharu Kobayashi, Shingo Ito
    TOHOKU MATHEMATICAL JOURNAL 64 (2) 223 - 231 0040-8735 2012/06 [Refereed][Not invited]
    We propose a new representation of the Schrodinger operator of a free particle by using the short-time Fourier transform and give its applications.
  • Masaharu Kobayashi, Akihiko Miyachi
    NAGOYA MATHEMATICAL JOURNAL 205 119 - 148 0027-7630 2012/03 [Refereed][Not invited]
    It is proved that the pseudodifferential operators sigma(t) (X, D) belong to the Schatten p-class C-p, 0 < p <= 2, the symbol sigma(x; omega) is in certain modulation spaees on R-x(d) x R-omega(d).
  • Application of wave packet transform to Schrödinger equations
    K.Kato, S. Ito, M.Kobayashi
    RIMS Kôkyûroku Bessatsu B33 29 - 39 2012 [Refereed][Not invited]
  • Remarks on Wiener amalgam space type estimates for Schrödinger equation
    K.Kato, M.Kobayashi, S. Ito
    RIMS Kôkyûroku Bessatsu B33 41 - 48 2012 [Refereed][Not invited]
  • Masaharu Kobayashi, Mitsuru Sugimoto
    JOURNAL OF FUNCTIONAL ANALYSIS 260 (11) 3189 - 3208 0022-1236 2011/06 [Refereed][Not invited]
    The inclusion relations between the L(p)-Sobolev spaces and the modulation spaces is determined explicitly. As an application, mapping properties of unimodular Fourier multiplier e(i|D|alpha) between L(p)-Sobolev spaces and modulation spaces are discussed. (C) 2011 Elsevier Inc. All rights reserved.
  • Remark on wave front sets of solutions to Schrödinger equation of a free particle and a harmonic oscillator
    K.Kato, M.Kobayashi, S. Ito
    SUT J. Math. 47 (2) 175 - 183 2011 [Refereed][Not invited]
    Masaharu Kobayashi, Yoshihiro Sawano
    OSAKA JOURNAL OF MATHEMATICS 47 (4) 1029 - 1053 0030-6126 2010/12 [Refereed][Not invited]
    The aim of this paper is to develop a theory of decomposition in the weighted modulation spaces M(p,q)(s,W) with 0 < p, q <= infinity, s is an element of R and W is an element of A(infinity), where W belongs to the class of A(infinity) defined by Muckenhoupt. For this purpose we shall define molecules for the modulation spaces. As an application we give a simple proof of the boundedness of the pseudo-differential operators with symbols in M(infinity,min(1,p,q))(0). We shall deal with dual spaces as well.
  • Modulation spaces and their applications
    Masaharu Kobayashi
    RIMS Kôkyûroku Bessatsu B22 131 - 135 2010 [Refereed][Not invited]
  • Masaharu Kobayashi, Mitsuru Sugimoto, Naohito Tomita
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 350 (1) 157 - 169 0022-247X 2009/02 [Refereed][Not invited]
    The results of [J.Sjostrand U. Sjostrand, An algebra of pseudodifferential operators, Math. Res. Lett. 1 (1994) 185-192] and Sugimoto [M. Sugimoto, L-p-boundedness of pseudo-differential operators satisfying Besov estimates, [J. Math. Soc. Japan 40 (1988) 105-122] oil a mapping property of pseudo-differential operators are two different kinds of extensions of the pioneering work by Calderon and Vaillancourt [A.P. Calderon, R. Vaillancourt, On the boundedness of pseudo-differential operators, J. Math. Soc. Japan 23 (1971) 374-378]. The objective of this paper is to show that these two results, which appeared to be independent ones, can be proved based on the same principle. For the purpose, we use the alpha-modulation spaces, a parameterized family of function spaces, which include Besov spaces and Modulation spaces as special cases. As an application, we also discuss the L-2- boundedness of the commutator [sigma(X. D),a]. where a(x) is a Lipschitz function and sigma belongs to an alpha-modulation space. (c) 2008 Elsevier Inc. All rights reserved.
  • Masaharu Kobayashi, Akihiko Miyachi, Naohito Tomita
    STUDIA MATHEMATICA 192 (1) 79 - 96 0039-3223 2009 [Refereed][Not invited]
    A sharp embedding relation between local Hardy spaces and modulation spaces is given.
  • Masaharu Kobayashi, Mitsuru Sugimoto, Naohito Tomita
    JOURNAL D ANALYSE MATHEMATIQUE 107 141 - 160 0021-7670 2009/01 [Refereed][Not invited]
    That symbols in the modulation space M (1,1) generate pseudo-differential operators of the trace class was first stated by Feichtinger and proved by Grochenig in [13]. In this paper, we show that the same is true if we replace M (1,1) by the more general alpha-modulation spaces, which include modulation spaces (alpha = 0) and Besov spaces (alpha = 1) as special cases. The result with alpha = 0 corresponds to that of Grochenig, and the one with alpha = 1 is a new result which states the trace property of the operators with symbols in the Besov space. As an application, we discuss the trace property of the commutator [alpha (X, D), a], where; a(chi) is a Lipschitz function and sigma(chi, xi) belongs to an alpha-modulation space.
  • Dual of modulation spaces
    Masaharu Kobayashi
    JOURNAL OF FUNCTION SPACES AND APPLICATIONS 5 (1) 1 - 8 0972-6802 2007 [Refereed][Not invited]
    We have constructed the modulation spaces M-p q (R (d)) in [2] for general 0 < p, q <= infinity , which coincide with the ususal modulation spaces when 1< p, q <= infinity, and studied their basic properties. The aim of this paper is the study of the dual of M-p,M-q (R (d)) for O<p,q<infinity. When 1 <= p,q<infinity, the fact that M-p',M-q' (R-d) is the dual of M-p,M-q(R-d) is already known, where 1/p + 1/p' = 1/q + 1/q' = 1. (See Feichtinger [1].) So in this paper we are concerned with the dual, in particular when p < 1 or q < 1. Motivated by the fact that the modulation spaces have similar properties to that of the Besov spaces (Proposition 2.2), we employ)J. Triebel's method [3] to study the dual. But gained results are similar to the sequence spaces V rather than the Besov spaces B-p,B-q (s)(R-d).
  • Modulation spaces M p,q for 0
    Masaharu Kobayashi
    J. Funct. Spaces Appl. 4 (3) 329 - 341 2006 [Refereed][Not invited]
  • Multipliers on modulation spaces
    Masaharu Kobayashi
    SUT J. Math. 42 (2) 305 - 312 2006 [Refereed][Not invited]

Books etc

  • ルベーグ積分 要点と演習
    相川 弘明, 小林政晴 (Joint work)
    共立出版 2018/09 (ISBN: 9784320113411) 244

Research Grants & Projects

  • モジュレーション空間とHRT予想の研究
    Date (from‐to) : 2019/04 -2022/03 
    Author : 小林政晴
  • モジュレーション空間とその偏微分方程式への応用
    文部科学省:科学研究費補助金(若手研究(B) )
    Date (from‐to) : 2016/04 -2019/03 
    Author : 小林政晴
  • 偏微分方程式に対するモジュレーション空間からのアプローチ
    文部科学省:科学研究費補助金(若手研究(B) )
    Date (from‐to) : 2012/04 -2015/03 
    Author : 小林政晴

Educational Activities

Teaching Experience

  • Vector Analysis
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 重積分,線積分,曲面積分,発散定理,ストークスの定理,div, rot, grad
  • Analysis C
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : シグマ加法族、測度、外測度, 可測関数、積分、エゴロフの定理、ルージンの定理、絶対連続測度、特異測度、ラドン・ニコディムの定理
  • Calculus I
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 数列, 収束, 関数, 極限, 微分, 偏微分, テイラ-の定理

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