Researcher Database

Naofumi Honda
Faculty of Science Mathematics Mathematics
Professor

Researcher Profile and Settings

Affiliation

  • Faculty of Science Mathematics Mathematics

Job Title

  • Professor

Degree

  • Doctor of Science(University of Tokyo)

J-Global ID

Research Interests

  • algebraic analysis   代数解析学   

Research Areas

  • Natural sciences / Basic analysis

Academic & Professional Experience

  • 2016/01 - Today Faculty of Science, Hokkaido University Department of Mathematics Professor

Education

  • 1988/04 - 1991/03  東京大学大学院
  • 1986/04 - 1988/03  東京大学大学院

Association Memberships

  • 日本数学会   

Research Activities

Published Papers

  • Hyperfunctions and Cech-Dolbeault cohomology in microlocal point of view
    N. Honda
    RIMS Koukyuroku 2101 (1) 7 - 12 2019/03 [Not refereed][Not invited]
  • On the Algebraic Study of Asymptotics
    N. Honda, L, Prelli
    Springer Proceedings in Mathematics & Statistics 256 (1) 227 - 238 2018/10 [Refereed][Not invited]
  • Uniqueness in the inverse boundary value problem for piecewise homogeneous anisotropic elasticity
    CĂTĂLIN I. CÂRSTEA, N. HONDA, Gen NAKAMURA
    SIAM J. Math. Anal. 50 (3) 3291 - 3302 2018/07 [Refereed][Not invited]
  • Naofumi Honda, Kohei Umeta
    Journal of the Mathematical Society of Japan 70 (1) 111 - 139 1881-1167 2018 [Refereed][Not invited]
     
    We establish an edge of the wedge theorem for the sheaf of holomorphic functions with exponential growth at infinity and construct the sheaf of Laplace hyperfunctions in several variables. We also study the fundamental properties of the sheaf of Laplace hyperfunctions.
  • On the theory of Laplace hyperfunctions in several variables
    HONDA Naofumi, Kohei Umeta
    RIMS Koukyuroku 2020 29 - 34 2017/04 [Not refereed][Not invited]
  • Generalization of multi-specializations and multi-asymptotics
    HONDA Naofumi, Luca Prelli
    RIMS Koukyuroku 2020 18 - 28 2017/04 [Not refereed][Not invited]
  • Apparent parameter technique and vanishing of cohomology groups with Whitney holomorphic functions
    HONDA Naofumi
    RIMS Koukyuroku 2020 10 - 17 2017/04 [Not refereed][Not invited]
  • Takashi Aoki, Naofumi Honda, Susumu Yamazaki
    Journal of the Mathematical Society of Japan 69 (4) 1715 - 1801 1881-1167 2017 [Refereed][Not invited]
     
    A new symbol theory for pseudodifferential operators in the complex analytic category is given. Here the pseudodifferential operators mean integral operators with real holomorphic microfunction kernels. The notion of real holomorphic microfunctions had been introduced by Sato, Kawai and Kashiwara by using sheaf cohomology theory. Symbol theory for those operators was partly developed by Kataoka and by the first author and it has been effectively used in the analysis of operators of infinite order. However, there was a missing part that links the symbol theory and the cohomological definition of operators, that is, the consistency of the Leibniz-Hörmander rule and the cohomological definition of composition for operators. This link has not been established completely in the existing symbol theory. This paper supplies the link and provides a cohomological foundation of the symbolic calculus of pseudodifferential operators.
  • An invitation to Sato's postulates in micro-analytic S-matrix theory
    HONDA Naofumi, KAWAI Takahiro
    RIMS Koukyuroku Bessatsu B61 23 - 56 2017/01 [Refereed][Not invited]
  • A study of pinch points and cusps in the Landau-Nakanishi geometry
    Naofumi Honda, Takahiro Kawai
    Kokyuroku Bessatsu B57 195 - 234 2016/09 [Refereed][Not invited]
  • Multi-microlocalization
    Naofumi Honda, Luca Prelli, Susumu Yamazaki
    Kokyuroku Bessatsu B57 93 - 116 2016/09 [Refereed][Not invited]
  • MULTI-MICROLOCALIZATION AND MICROSUPPORT
    Naofumi Honda, Luca Prelli, Susumu Yamazaki
    BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE 144 (3) 569 - 611 0037-9484 2016 [Refereed][Not invited]
     
    The purpose of this paper is to establish the foundations of multi-microlocalization, in particular, to give the fiber formula for the multi-microlocalization functor and estimate of microsupport of a multi-microlocalized object. We also give some applications of these results.
  • Kernel functions and symbols of pseudodifferential operators of infinite order with an apparent parameter
    T. Aoki, N.Honda, S.Yamazaki
    RIMS Koukyuroku Bessatsu B52 175 - 192 2015/06 [Refereed][Not invited]
  • On the sheaf of Laplace hyperfunctions in several variables
    N. Honda, K. Umeta
    RIMS Koukyuroku Bessatsu B52 213 - 218 2015/06 [Refereed][Not invited]
  • On the geometric aspect of Sato's postulates on the S-matrix
    N. Honda, T. Kawai, H. P. Stapp
    RIMS Koukyuroku bessatsu B52 11 - 53 2015/06 [Refereed][Not invited]
  • Naofumi Honda, Joyce McLaughlin, Gen Nakamura
    INVERSE PROBLEMS 30 (5) 1 - 19 0266-5611 2014/05 [Refereed][Not invited]
     
    An inverse problem to identify unknown coefficients of a partial differential equation by a single interior measurement is considered. The equation considered in this paper is a strongly elliptic second order scalar equation which can have complex coefficients in a bounded domain with C-2 boundary. We are given a single interior measurement. This means that we know a given solution of the forward equation in this domain. The equation includes some model equations arising from acoustics, viscoelasticity and hydrology. We assume that the coefficients are piecewise analytic. Our major result is the local Holder stability estimate for identifying the unknown coefficients. If the unknown coefficient is a complex coefficient in the principal part of the equation, we assumed a condition which we name admissibility assumption for the real part and imaginary part of the difference of two complex coefficients. This admissibility assumption is automatically satisfied if the complex coefficients are real valued. For identifying either the real coefficient in the principal part or the coefficient of the 0th order of the equation, the major result implies global uniqueness for the identification.
  • A computer-assisted study of the Landau-Nakanishi Geometry
    Naofumi Honda, Takahiro Kawai
    RIMS Koukyuroku 1861 100 - 110 2014 [Not refereed][Not invited]
  • On kernel functions and symbols of analytic pseudo-differential operators
    T.Aoki, N.Honda, S.Yamazaki
    RIMS Koukyuroku 1835 21 - 37 2013/08 [Not refereed][Not invited]
  • On the number of the turning points of the second kind of the Noumi-Yamada systems with a large parameter
    T. Aoki, N. Honda, Y. Umeta
    RIMS Koukyuroku Bessatsu B37 1 - 30 2013/08 [Refereed][Invited]
  • Takashi Aoki, Naofumi Honda, Yoko Umeta
    Advances in Mathematics 235 496 - 524 0001-8708 2013/03/01 [Refereed][Not invited]
     
    We construct general formal solutions containing sufficiently many free parameters for the first Painlevé hierarchy with a large parameter from a viewpoint of the multiple-scale analysis. © 2012 Elsevier Ltd.
  • N. Honda, G. Nakamura, M. Sini
    Mathematische Annalen 355 (2) 401 - 427 0025-5831 2013 [Refereed][Not invited]
     
    We deal with an inverse obstacle problem for general second order scalar elliptic operators with real principal part and analytic coefficients near the obstacle. We assume that the boundary of the obstacle is a non-analytic hypersurface. We show that, when we put Dirichlet boundary conditions, one measurement is enough to reconstruct the obstacle. In the Neumann case, we have results only for n = 2, 3 in general. More precisely, we show that one measurement is enough for n = 2 and we need 3 linearly independent inputs for n = 3. However, in the case for the Helmholtz equation, we only need n - 1 linearly independent inputs, for any n ≥ 2. Here n is the dimension of the space containing the obstacle. These are justified by investigating the analyticity properties of the zero set of a real analytic function. In addition, we give a reconstruction procedure for each case to recover the shape of obstacle. Although we state the results for the scattering problems, similar results are true for the associated boundary value problems. © 2012 Springer-Verlag.
  • Naofumi Honda, Luca Prelli
    ADVANCES IN MATHEMATICS 232 (1) 432 - 498 0001-8708 2013/01 [Refereed][Not invited]
     
    In this paper we extend the notion of specialization functor to the case of several closed submanifolds satisfying some suitable conditions. Applying this functor to the sheaf of Whitney holomorphic functions we construct different kinds of sheaves of multi-asymptotically developable functions, whose definitions are natural extensions of the definition of strongly asymptotically developable functions introduced by Majima. (C) 2012 Elsevier Inc. All rights reserved.
  • On the Sheaf of Laplace Hyperfunctions with Holomorphic Parameters
    Naofumi Honda, Kohei Umeta
    JOURNAL OF MATHEMATICAL SCIENCES-THE UNIVERSITY OF TOKYO 19 (4) 559 - 586 1340-5705 2012 [Refereed][Not invited]
     
    We give a vanishing theorem of cohomology groups on a pseudoconvex open subset for holomorphic functions with exponential growth at infinity. As an application, we construct the sheaf of Laplace hyperfunctions and that with holomorphic parameters, and we also study several properties of these sheaves.
  • On the form of instanton-type solutions for equations of the first Painleve' hierarchy by multiple-scale analysis
    T. Aoki, N. Honda, Y. Umeta
    Rend. Sem. Mat. Univ. Politec. Torino 69 (4) 331 - 338 2012 [Refereed][Not invited]
  • Cohomology vanishing theorem and Laplace hyperfunctions with holomoprhic parameters
    H. Naofumi, K. Umeta
    Rend. Sem. Mat. Univ. Politec. Torino 69 (4) 347 - 353 2012 [Refereed][Not invited]
  • Naofumi Honda, Luca Prelli
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 87 (5) 69 - 72 0386-2194 2011/05 [Refereed][Not invited]
     
    We extend the notion of specialization functor to the case of several closed submanifolds satisfying some suitable conditions. Applying this functor to the sheaf of Whitney holomorphic functions we construct different kinds of sheaves of multi-asymptotically developable functions, whose definitions are natural extensions of the definition of strongly asymptotically developable functions introduced by Majima.
  • Takashi Aoki, Naofumi Honda
    Journal of the Mathematical Society of Japan 63 (4) 1085 - 1119 0025-5645 2011 [Refereed][Not invited]
     
    The system of algebraic equations for the leading terms of formal solutions to the Noumi-Yamada systems with a large parameter is studied. A formula which gives the number of solutions outside of turning points is established. The number of turning points of the first kind is also given. © 2011 The Mathematical Society of Japan.
  • STRATIFIED WHITNEY JETS AND TEMPERED ULTRADISTRIBUTIONS ON THE SUBANALYTIC SITE
    N. Honda, G. Morando
    BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE 139 (3) 389 - 435 0037-9484 2011 [Refereed][Not invited]
     
    In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold X. Then, we define stratified ultradistributions of Beurling and Roumieu type on X. In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if X is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to X. Second, the tempered-stratified ultradistributions on the complementary of a 1-regular closed subset of X coincide with the sections of the presheaf of tempered ultradistributions.
  • The geometric structure of a virtual turing point and the motel of the Stokes geometry
    Naofumi Honda
    RIMS Kokyuroku Bessatsu B10 63 - 117 2009/12 [Refereed][Not invited]
  • N. Honda, G. Nakamura, R. Potthast, M. Sini
    Ann. Math. Pura Appl. 187 188 - 215 2008 [Refereed][Not invited]
  • Takashi Aoki, Naofumi Honda
    Proceedings of the Japan Academy Series A: Mathematical Sciences 84 (3) 42 - 47 0386-2194 2008 [Refereed][Not invited]
     
    The notion of principally tame regular sequences is introduced for systems of polynomials with a weight vector. As an application, construction of formal solutions is discussed for the systems of nonlinear differential equations which belong to the fourth Painlevé hierarchy with a large parameter. © 2008 The Japan Academy.
  • Takashi Aoki, Naofumi Honda, Takahiro Kawai, Tatsuya Koike, Yukihiro Nishikawa, Shunsuke Sasaki, Akira Shudo, Yoshitsugu Takei
    Algebraic Analysis of Differential Equations: From Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai 29 - 43 2008 [Refereed][Not invited]
     
    Several aspects of the notion of virtual turning points are discussed its background, its relevance to the bifurcation phenomena of a Stokes curve, its importance in the analysis of the Noumi-Yamada system (a particular higher order Painlevé equation) and a concrete recipe for locating them. Examples given here make it manifest that virtual turning points are indispensable in WKB analysis of higher order linear ordinary differential equations with a large parameter. © 2008 Springer Japan.
  • Virtual turning points
    T.Aoki, N. Honda, T. Kawai, T. Koike, N. Nishikawa, S. Sasaki, A. Shudo, Y. Takei
    Algebraic Analysis of Differential Equations, Springer 29 - 44 2007 [Refereed][Not invited]
  • On the Stokes geometry of the Noumi-Yamada system
    Naofumi Honda
    RIMS Kokyuroku Bessatsu B2 45 - 72 2007 [Refereed][Not invited]
  • Degenerate Stokes geometry and some geometric structure underlying a virtual turning point
    Naofumi Honda
    RIMS Kokyuroku Bessatsu B5 15 - 49 2007 [Refereed][Not invited]
  • T. Aoki, N. Honda
    Algebraic Analysis of Differential Equations, Springer 45 - 55 2007 [Refereed][Not invited]
  • On the algebraic equations associated with Noumi-Yamada Systems
    T. Aoki, N.Honda
    RIMS Koukyuroku 1516 1 - 11 2006 [Not refereed][Not invited]
  • On the examples of Stokes geometry for Noumi-Yamada systems
    Naofumi Honda
    数理解析研究所 講究録 1516 24 - 167 2006 [Not refereed][Not invited]
  • Microlocal Stokes phenomena for holonomic modules
    Naofumi Honda
    Toward the Exact WKB Analysis of Differential Equations 33 - 39 2000 [Refereed][Not invited]
  • Regularity theorems for holonomic modules
    Naofumi Honda
    Proc.Banach Center publ. 33 85 - 91 1996 [Refereed][Not invited]
  • Microfunction Solutions of Holonomic Systems and Stokes Lines
    Naofumi Honda
    Structure of Solutions of Differential Equations, World Scientific 169 - 182 1996 [Refereed][Not invited]
  • REGULARITY THEOREMS FOR HOLONOMIC MODULES
    N HONDA
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 69 (5) 111 - 114 0386-2194 1993/05 [Refereed][Not invited]
  • Solvability of ordinary differential equations in the space of distributions
    HONDA Naofumi
    J. Fac. Sci. Univ. Tokyo 39 207 - 232 1992 [Refereed][Not invited]
  • On the D modules described by the inverse image of the smooth map
    Naofumi Honda
    J. Fac. Sci. Univ. Tokyo 38 351 - 358 1991 [Refereed][Not invited]
  • Naofumi Honda
    Publ. RIMS, Kyoto Univ 27 923 - 943 1991 [Refereed][Not invited]
  • A VANISHING THEOREM FOR HOLONOMIC MODULES WITH POSITIVE CHARACTERISTIC VARIETIES
    N HONDA, P SCHAPIRA
    PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES 26 (3) 529 - 534 0034-5318 1990/10 [Refereed][Not invited]

Books etc

  • Virtual turning points, Springer briefs in Mathematical Physics, 4
    N. Honda, T.Kawai, Y.Takei (Joint work)
    Springer 2015/07
  • General topology
    Shuichi Jimbo, Naofumi Honda (Joint work)
    Suugaku Shyobou 2010/04

Conference Activities & Talks

  • Čech-Dolbeault cohomology and hyperfunctions  [Invited]
    HONDA Naofumi
    微分方程式の総合的研究 全体講演  2018/12
  • 仮想変わり点の幾何とストークス係数,  [Invited]
    本多 尚文
    2010年度日本数学会秋季大会函数方程式分科会特別講演  2010
  • 不確定特異点型極大過剰決定系の解の構造について  [Invited]
    本多 尚文
    1996年度日本数学会春季大会函数解析分科会特別講演  1996

Research Grants & Projects

  • 不確定特異点型の極大過剰決定系の研究
  • On the structure of the holonomic systems

Educational Activities

Teaching Experience

  • Topics in Mathematical Analysis A
    開講年度 : 2018
    課程区分 : 修士課程
    開講学部 : 理学院
    キーワード : 層,帰納極限, 帰納層
  • Topics in Mathematical Analysis B
    開講年度 : 2018
    課程区分 : 修士課程
    開講学部 : 理学院
    キーワード : 層,帰納極限, 帰納層
  • Inter-Graduate School Classes(General Subject):Natural and Applied Sciences
    開講年度 : 2018
    課程区分 : 修士課程
    開講学部 : 大学院共通科目
    キーワード : 層,帰納極限, 帰納層
  • Analysis G
    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 : フーリエ級数, p乗可積分空間, 急減少関数, フーリエ変換, ソボレフ空間
  • Advanced Mathematical 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 : 層,帰納極限, 帰納層
  • Linear Algebra 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 : 行列, 連立1次方程式, 基本変形, 階数, 行列式, 逆行列
  • Exercises on Basic Mathematics D
    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 : 多変数関数, 偏微分, テーラーの定理, 逆写像定理, 陰関数定理, 重積分,広義積分


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