基本情報

所属

• 理学研究院　数学部門　数学分野

職名

• 准教授

学位

• 博士(理学)（東京理科大学）

ホームページURL

https://kaken.nii.ac.jp/d/r/30516480.ja.html

J-Global ID

• 201501044561299580

研究キーワード

• 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   

研究分野

• 自然科学一般 / 基礎解析学

担当教育組織

•  学士課程　理学部
•  修士課程　理学院
•  博士課程　理学院

職歴

• 2012年 東京理科大学 理学部 助教

所属学協会

• 日本数学会   

研究活動情報

論文

• A note on operating functions of modulation spaces

  Masaharu Kobayashi, Enji Sato

  Journal of Pseudo-Differential Operators and Applications 13 4 2022年12月 [査読有り]
  
• Operating Functions on $$A^q_s({ { \mathbf {T } } })$$

  Masaharu Kobayashi, Enji Sato

  Journal of Fourier Analysis and Applications 28 3 2022年06月 [査読有り]
  
• Representation of higher-order dispersive operators via short-time Fourier transform and its application

  Keiichi Kato, Masaharu Kobayashi, Shingo Ito, Tadashi Takahashi

  Tohoku Mathematical Journal 73 1 105 - 118 2021年03月 [査読有り]
  
• Operating functions on modulation and Wiener amalgam spaces

  小林政晴, 佐藤圓治

  Nagoya Math. J. 230 72 - 82 2018年 [査読有り][通常論文]
  
• REMARK ON CHARACTERIZATION OF WAVE FRONT SET BY WAVE PACKET TRANSFORM

  Keiichi Kato, Masaharu Kobayashi, Shingo Ito

  OSAKA JOURNAL OF MATHEMATICS 54 2 209 - 228 2017年04月 [査読有り][通常論文]
   

  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年 [査読有り][通常論文]
  
• Inclusion relations between L-P-Sobolev and Wiener amalgam spaces

  Jayson Cunanan, Masaharu Kobayashi, Mitsuru Sugimoto

  JOURNAL OF FUNCTIONAL ANALYSIS 268 1 239 - 254 2015年01月 [査読有り][通常論文]
   

  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

  Keiichi Kato, Masaharu Kobayashi, Shingo Ito

  NONLINEAR DYNAMICS IN PARTIAL DIFFERENTIAL EQUATIONS 64 417 - 425 2015年 [査読有り][通常論文]
   

  We introduce the wave front set WFsp,q by using the wave packet transform. This is another characterization of the Fourier Lebesgue type wave front set WFFLqs. We apply this to the propagation of singularities for the wave equation.
• Estimates on modulation spaces for Schrödinger evolution operators with quadratic and sub-quadratic potentials

  K.Kato, M.Kobayashi, S. Ito

  J. Funct. Anal. 266 2 733 - 753 2014年01月 [査読有り][通常論文]
   

  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 2013年04月 [査読有り][通常論文]
   

  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.
• Representation of Schrödinger operator of a free particle via short-time Fourier transform and its applications

  K.Kato, M.Kobayashi, S.Ito

  Tohoku Math. J. (2) 64 2 223 - 231 2012年06月 [査読有り][通常論文]
   

  We propose a new representation of the Schrodinger operator of a free particle by using the short-time Fourier transform and give its applications.
• SCHATTEN p-CLASS PROPERTY OF PSEUDODIFFERENTIAL OPERATORS WITH SYMBOLS IN MODULATION SPACES

  Masaharu Kobayashi, Akihiko Miyachi

  NAGOYA MATHEMATICAL JOURNAL 205 119 - 148 2012年03月 [査読有り][通常論文]
   

  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 京都大学 2012年 [査読有り][通常論文]
  
• Remarks on Wiener amalgam space type estimates for Schrödinger equation

  K.Kato, M.Kobayashi, S.Ito

  RIMS Kôkyûroku Bessatsu B33 41 - 48 京都大学 2012年 [査読有り][通常論文]
  
• The inclusion relation between Sobolev and modulation spaces

  Masaharu Kobayashi, Mitsuru Sugimoto

  JOURNAL OF FUNCTIONAL ANALYSIS 260 11 3189 - 3208 2011年06月 [査読有り][通常論文]
   

  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年 [査読有り][通常論文]
  
• MOLECULAR DECOMPOSITION OF THE MODULATION SPACES

  Masaharu Kobayashi, Yoshihiro Sawano

  OSAKA JOURNAL OF MATHEMATICS 47 4 1029 - 1053 2010年12月 [査読有り][通常論文]
   

  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

  小林政晴

  RIMS Kôkyûroku Bessatsu B22 131 - 135 2010年 [査読有り][通常論文]
  
• On the L 2 -boundedness of pseudo-differential operators and their commutators with symbols in α -modulation spaces

  M.Kobayashi, M.Sugimoto, N.Tomita

  J. Math. Anal. Appl. 350 1 157 - 169 2009年02月 [査読有り][通常論文]
   

  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.
• Embedding relations between local Hardy and modulation spaces

  Masaharu Kobayashi, Akihiko Miyachi, Naohito Tomita

  STUDIA MATHEMATICA 192 1 79 - 96 2009年 [査読有り][通常論文]
   

  A sharp embedding relation between local Hardy spaces and modulation spaces is given.
• Trace ideals for pseudo-differential operators and their commutators with symbols in α -modulation spaces

  M.Kobayashi, M.Sugimoto, N.Tomita

  J. Anal. Math. 107 141 - 160 2009年01月 [査読有り][通常論文]
   

  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 2007年 [査読有り][通常論文]
   

  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

  小林政晴

  J. Funct. Spaces Appl. 4 3 329 - 341 2006年 [査読有り][通常論文]
  
• Multipliers on modulation spaces

  小林政晴

  SUT J. Math. 42 2 305 - 312 2006年 [査読有り][通常論文]