Edit Profile (opens in new tab) Kawai, Takahiro Co-Author Distance Author ID: kawai.takahiro Published as: Kawai, Takahiro; Kawai, T. Homepage: http://www.kurims.kyoto-u.ac.jp/en/list/KAWAI,%20Takahiro.html External Links: Wikidata · GND · IdRef Documents Indexed: 161 Publications since 1970, including 4 Books 10 Contributions as Editor · 2 Further Contributions Biographic References: 4 Publications Co-Authors: 40 Co-Authors with 129 Joint Publications 1,422 Co-Co-Authors all top 5 Co-Authors 43 single-authored 55 Takei, Yoshitsugu 49 Kashiwara, Masaki 24 Aoki, Takashi 13 Koike, Tatsuya 9 Stapp, Henry P. 7 Kamimoto, Shingo 6 Struppa, Daniele Carlo 5 Honda, Naofumi 4 Oshima, Toshio 4 Sato, Mikio 3 Berenstein, Carlos Alberto 2 Hirose, Sampei 2 Kimura, Tatsuo 2 Komatsu, Hikosaburo 2 Miwa, Tetsuji 2 Morimoto, Mitsuo 2 Nakamura, Gen 2 Nishikawa, Yukihiro 2 Noumi, Masatoshi 2 Sasaki, Shunsuke 2 Shudo, Akira 2 Sjöstrand, Johannes 1 Adamatzky, Andrew I. 1 Andronikof, Emmanuel 1 Bedford, Eric 1 Ehrenpreis, Leon 1 Enomoto, Hikoe 1 Farkas, Hershel M. 1 Fujimoto, Yoshihisa 1 Fujita, Keiko 1 Guillemin, Victor W. 1 Gunji, Yukio-Pegio 1 Hitotumatu, Sin 1 Howls, Christopher John 1 Ihara, Yasutaka 1 Ion, Patrick D. F. 1 Ishii, Tadashi 1 Jimbo, Michio 1 Kataoka, Kiyoomi 1 Kuchment, Peter A. 1 Kurokawa, Nobushige 1 Matsuzawa, Tadato 1 McCoy, Barry M. 1 Mulase, Motohico 1 Murakami, Hisashi 1 Namba, Kanji 1 Niizato, Takayuki 1 Quinto, Eric Todd 1 Sasaki, Shinji 1 Schapira, Pierre 1 Sogawa, Harue 1 Sternberg, Shlomo 1 Sugiura, Mitsuo 1 Takasaki, Kanehisa 1 Taylor, Alan M. 1 Tracy, Craig Arnold 1 Uchikoshi, Keisuke 1 Ueno, Kenji 1 Yano, Tamaki 1 Yau, Shing-Tung all top 5 Serials 21 Publications of the Research Institute for Mathematical Sciences, Kyoto University 18 Proceedings of the Japan Academy 13 Advances in Mathematics 12 RIMS Kokyuroku 10 Proceedings of the Japan Academy. Series A 6 RIMS Kôkyûroku Bessatsu 4 Communications in Mathematical Physics 4 Journal of the Mathematical Society of Japan 3 Journal of the Faculty of Science. Section I A 3 RIMS Kokyuroku 2 Annales de l’Institut Fourier 2 Journal of Mathematics of Kyoto University 2 Proceedings of the American Mathematical Society 2 Journal of Physics A: Mathematical and General 2 Notices of the American Mathematical Society 2 The Asian Journal of Mathematics 1 Communications on Pure and Applied Mathematics 1 Journal of Mathematical Physics 1 Letters in Mathematical Physics 1 Arkiv för Matematik 1 American Journal of Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Funkcialaj Ekvacioj. Serio Internacia 1 Sūgaku 1 Sugaku Expositions 1 International Journal of Mathematics 1 Bulletin of the American Mathematical Society 1 Annals of Mathematics Studies 1 Princeton Mathematical Series 1 Translations of Mathematical Monographs 1 Kyoto Journal of Mathematics 1 SpringerBriefs in Mathematical Physics all top 5 Fields 87 Partial differential equations (35-XX) 55 Ordinary differential equations (34-XX) 34 Several complex variables and analytic spaces (32-XX) 30 Global analysis, analysis on manifolds (58-XX) 27 Functional analysis (46-XX) 27 Quantum theory (81-XX) 15 Operator theory (47-XX) 13 Algebraic geometry (14-XX) 11 General and overarching topics; collections (00-XX) 7 Special functions (33-XX) 6 History and biography (01-XX) 4 Functions of a complex variable (30-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Numerical analysis (65-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Mechanics of particles and systems (70-XX) 2 Number theory (11-XX) 2 Algebraic topology (55-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) 1 Differential geometry (53-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 128 Publications have been cited 1,398 times in 787 Documents Cited by ▼ Year ▼ Microfunctions and pseudo-differential equations. Zbl 0277.46039 Sato, Mikio; Kawai, Takahiro; Kashiwara, Masaki 319 1973 On holonomic systems of microdifferential equations. III: Systems with regular singularities. Zbl 0505.58033 Kashiwara, Masaki; Kawai, Takahiro 119 1981 Algebraic analysis of singular perturbation theory. Transl. from the Japanese by Goro Kato. Zbl 1100.34004 Kawai, Takahiro; Takei, Yoshitsugu 76 2005 On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients. Zbl 0212.46101 Kawai, Takahiro 54 1970 Foundations of algebraic analysis. Transl. from the Japanese by Goro Kato. Zbl 0605.35001 Kashiwara, Masaki; Kawai, Takahiro; Kimura, Tatsuo 47 1986 Second-microlocalization and asymptotic expansions. Zbl 0458.46027 Kashiwara, Masaki; Kawai, Takahiro 36 1980 The Bender-Wu analysis and the Voros theory. Zbl 0782.35060 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 31 1991 The Poincaré lemma for variations of polarized Hodge structure. Zbl 0629.14005 Kashiwara, Masaki; Kawai, Takahiro 31 1987 Micro-hyperbolic pseudo-differential operators. I. Zbl 0305.35066 Kashiwara, Masaki; Kawai, Takahiro 29 1975 On the boundary value problem for elliptic system of linear differential equations. I. Zbl 0271.35028 Kashiwara, Masaki; Kawai, Takahiro 26 1972 Boundary values of hyperfunction solutions of linear partial differential equations. Zbl 0225.35032 Komatsu, Hikosaburo; Kawai, Takahiro 24 1971 Virtual turning points. Zbl 1354.34003 Honda, Naofumi; Kawai, Takahiro; Takei, Yoshitsugu 23 2015 New turning points in the exact WKB analysis for higher-order ordinary differential equations. Zbl 0831.34058 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 21 1994 The Bender-Wu analysis and the Voros theory. II. Zbl 1175.34112 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 20 2009 WKB analysis of Painlevé transcendents with a large parameter. I. Zbl 0848.34005 Kawai, Takahiro; Takei, Yoshitsugu 16 1996 On the Stokes geometry of higher order Painlevé equations. Zbl 1086.34072 Kawai, Takahiro; Koike, Tatsuya; Nishikawa, Yukihiro; Takei, Yoshitsugu 16 2004 On a class of linear partial differential equations whose formal solutions always converge. Zbl 0411.35003 Kashiwara, Masaki; Kawai, Takahiro; Sjöstrand, Johannes 16 1979 Holonomic systems of linear differential equations and Feynman integrals. Zbl 0449.35095 Kashiwara, Masaki; Kawai, Takahiro 16 1977 WKB analysis of Painlevé transcendents with a large parameter. II: Multiple-scale analysis of Painlevé transcendents. Zbl 0894.34050 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 15 1996 WKB analysis of Painlevé transcendents with a large parameter. III: Local reduction of 2-parameter Painlevé transcendents. Zbl 0901.34057 Kawai, Takahiro; Takei, Yoshitsugu 15 1998 On holonomic systems for \(\prod_{l=1}^N(f_l+\sqrt{-1}0)^{\lambda_l}\). Zbl 0449.35067 Kashiwara, Masaki; Kawai, Takahiro 15 1979 Construction of local elementary solutions for linear partial differential operators with real analytic coefficients. I: The case with real principal symbols. Zbl 0216.12303 Kawai, Takahiro 15 1971 On the characteristic variety of a holonomic system with regular singularities. Zbl 0449.58019 Kashiwara, Masaki; Kawai, Takahiro 13 1979 On the exact WKB analysis of operators admitting infinitely many phases. Zbl 1056.34103 Aoki, Takashi; Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu 13 2004 Virtual turning points and bifurcation of Stokes curves for higher order ordinary differential equations. Zbl 1073.34098 Aoki, Takashi; Kawai, Takahiro; Sasaki, Shunsuke; Shudo, Akira; Takei, Yoshitsugu 12 2005 Algebraic analysis of singular perturbations – on exact WKB analysis. Zbl 0871.32015 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 10 1993 Hodge structure and holonomic systems. Zbl 0629.14006 Kashiwara, Masaki; Kawai, Takahiro 9 1986 Linear Differential equations of infinite order and theta functions. Zbl 0546.35047 Sato, Mikio; Kashiwara, Masaki; Kawai, Takahiro 8 1983 On the boundary value problem for elliptic system of linear differential equations. II. Zbl 0279.35037 Kashiwara, Masaki; Kawai, Takahiro 8 1973 Theory of vector-valued hyperfunctions. Zbl 0321.46033 Ion, Patrick D. F.; Kawai, Takahiro 8 1975 Finiteness theorem for holonomic systems of micro-differential equations. Zbl 0361.35064 Kashiwara, Masaki; Kawai, Takahiro 8 1976 A study of Feynman integrals by micro-differential equations. Zbl 0392.46025 Kashiwara, Masaki; Kawai, Takahiro; Oshima, Toshio 8 1978 On the WKB-theoretic structure of a Schrödinger operator with a merging pair of a simple pole and a simple turning point. Zbl 1201.34141 Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu 8 2010 The Fabry-Ehrenpreis gap theorem and linear differential equations of infinite order. Zbl 0618.30003 Kawai, Takahiro 8 1987 On the exact WKB analysis for the third order ordinary differential equations with a large parameter. Zbl 0963.34045 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 8 1998 Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point. I: Its WKB-theoretic transformation to the Mathieu equation. Zbl 1293.35300 Kamimoto, Shingo; Kawai, Takahiro; Takei, Yoshitsugu 8 2014 Structure of cohomology groups whose coefficients are microfunction solution sheaves of systems of pseudo-differential equations with multiple characteristics. I. Zbl 0307.35081 Kashiwara, Masaki; Kawai, Takahiro; Oshima, Toshio 7 1974 Discontinuity formula and Sato’s conjecture. Zbl 0368.35067 Kawai, Takahiro; Stapp, Henry P. 7 1977 Interpolating varieties and the Fabry-Ehrenpreis-Kawai gap theorem. Zbl 0890.32007 Berenstein, C. A.; Kawai, T.; Struppa, D. C. 7 1996 On a class of linear differential operators of infinite order with finite index. Zbl 0628.35003 Aoki, Takashi; Kashiwara, Masaki; Kawai, Takahiro 7 1986 Microlocal analysis of theta functions. Zbl 0603.10023 Sato, Mikio; Kashiwara, Masaki; Kawai, Takahiro 7 1984 Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point. II: Its relevance to the Mathieu equation and the Legendre equation. Zbl 1293.35301 Kamimoto, Shingo; Kawai, Takahiro; Takei, Yoshitsugu 7 2014 On the exact steepest descent method: a new method for the description of Stokes curves. Zbl 1063.34047 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 7 2001 Microlocal analysis. Zbl 0536.58030 Kashiwara, Masaki; Kawai, Takahiro 6 1983 On a conjecture of Regge and Sato on Feynman integrals. Zbl 0347.35061 Kashiwara, Masaki; Kawai, Takahiro 6 1976 On the structure of single linear pseudo-differential equations. Zbl 0297.35069 Sato, Mikio; Kawai, Takahiro; Kashiwara, Masaki 6 1972 Seminar on micro-local analysis. Zbl 0409.00007 Guillemin, Victor W.; Kashiwara, Masaki; Kawai, Takahiro 6 1979 Some applications of boundary value problems for elliptic systems of linear differential equations. Zbl 0454.46033 Kashiwara, Masaki; Kawai, Takahiro 6 1979 WKB analysis of higher order Painlevé equations with a large parameter – local reduction of 0-parameter solutions for Painlevé hierarchies \((P_{J})\) (\(J=\text{ I, II-1 or II-2}\)). Zbl 1108.34065 Kawai, Takahiro; Takei, Yoshitsugu 6 2006 On the existence of holomorphic solutions of systems of linear differential equations of infinite order and with constant coefficients. Zbl 0704.35015 Kawai, Takahiro; Struppa, Daniele C. 6 1990 Micro-analytic structure of the S-matrix and related functions. Zbl 0443.35059 Kashiwara, Masaki; Kawai, Takahiro; Stapp, Henry P. 6 1977 Exact WKB analysis of non-adiabatic transition probabilities for three levels. Zbl 1027.81010 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 6 2002 On the global existence of real analytic solutions of linear differential equations. I. Zbl 0234.35012 Kawai, T. 6 1972 Construction of elementary solutions for I-hyperbolic operators and solutions with small singularities. Zbl 0216.12301 Kawai, Takahiro 6 1970 Secular equations through the exact WKB analysis. Zbl 0834.34068 Kawai, Takahiro; Takei, Yoshitsugu 5 1994 Extension of solutions of systems of linear differential equations. Zbl 0366.58013 Kawai, Takahiro 5 1976 Holonomic character and local monodromy structure of Feynman integrals. Zbl 0367.46039 Kashiwara, Masaki; Kawai, Takahiro 5 1977 Theorems on the finite-dimensionality of cohomology groups. IV. Zbl 0303.35057 Kawai, Takahiro 5 1973 On the exact WKB analysis of microdifferential operators of WKB type. Zbl 1079.34070 Aoki, Takashi; Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu 5 2004 On the regular holonomic character of the S-matrix and microlocal analysis of unitarity-type integrals. Zbl 0491.35066 Kawai, Takahiro; Stapp, Henry P. 5 1982 Finite-dimensionality of cohomology groups attached to systems of linear differential equations. Zbl 0256.35059 Kawai, Takahiro 5 1973 Overconvergence phenomena and grouping in exponential representation of solutions of linear differential equations of infinite order. Zbl 0984.30003 Kawai, Takahiro; Struppa, Daniele C. 5 2001 The Poincaré lemma for a variation of polarized Hodge structure. Zbl 0576.14010 Kashiwara, Masaki; Kawai, Takahiro 4 1985 Theorems on the finite-dimensionality of cohomology groups. III. Zbl 0303.35056 Kawai, Takahiro 4 1973 Micro-local properties of \(\prod^n_{j=1}f^{S_j}_{j^+}\). Zbl 0304.35068 Kashiwara, Masaki; Kawai, Takahiro 4 1975 Pseudo-differential operators in the theory of hyperfunctions. Zbl 0229.47034 Kashiwara, Masaki; Kawai, Takahiro 4 1970 Microlocal properties of local elementary solutions for Cauchy problems for a class of hyperbolic linear differential operators. Zbl 0389.35032 Kawai, Takahiro; Nakamura, Gen 3 1978 Infrared catastrophe in a massless Feynman function. Zbl 0809.46088 Kawai, T.; Stapp, H. P. 3 1993 Virtual turning points – a gift of microlocal analysis to the exact WKB analysis. Zbl 1145.34383 Aoki, Takashi; Honda, Naofumi; Kawai, Takahiro; Koike, Tatsuya; Nishikawa, Yukihiro; Sasaki, Shunsuke; Shudo, Akira; Takei, Yoshitsugu 3 2007 Micro-local analysis of Feynman amplitudes. Zbl 0454.46034 Kashiwara, Masaki; Kawai, Takahiro 3 1979 Poisson’s summation formula and Hamburger’s theorem. Zbl 0499.10042 Ehrenpreis, Leon; Kawai, Takahiro 3 1982 Microlocal analysis of fixed singularities of WKB solutions of a Schrödinger equation with a merging triplet of two simple poles and a simple turning point. Zbl 1279.34105 Kamimoto, Shingo; Kawai, Takahiro; Takei, Yoshitsugu 3 2012 WKB analysis of higher order Painlevé equations with a large parameter. II. Structure theorem for instanton-type solutions of \((P_J)_m (J= I, 34\), II-2 or IV) near a simple \(P\)-turning point of the first kind. Zbl 1228.34144 Kawai, Takahiro; Takei, Yoshitsugu 3 2011 On the exact WKB analysis of higher order simple-pole type operators. Zbl 1231.34155 Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu 3 2011 On the boundary value of a solution of the heat equation. Zbl 0696.35066 Kawai, Takahiro; Matsuzawa, Tadato 3 1989 Micro-analyticity of the S-matrix and related functions. Zbl 0424.35078 Kashiwara, Masaki; Kawai, Takahiro; Stapp, Henry P. 3 1979 The theory of holonomic systems with regular singularities and its relevance to physical problems. Zbl 0459.70013 Kashiwara, Masaki; Kawai, Takahiro 3 1980 The exact steepest descent method – a new steepest descent method based on the exact WKB analysis. Zbl 1072.34105 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 3 2004 Theorems on the finite -dimensionality of cohomology groups. I. Zbl 0249.58014 Kawai, Takahiro 3 1972 Construction of a local elementary solution for linear partial differential operators. I, II. Zbl 0216.12302 Kawai, Takahiro 3 1971 An example of a complex of linear differential operators of infinite order. Zbl 0525.35082 Kawai, Takahiro 2 1983 The Fabry-Ehrenpreis gap theorem for hyperfunctions. Zbl 0554.46017 Kawai, Takahiro 2 1984 Exponential representation of a holomorphic solution of a system of differential equations associated with the theta-zerovalue. Zbl 0973.35055 Berenstein, Carlos A.; Kawai, Takahiro; Struppa, Daniele C.; Takei, Yoshitsugu 2 1996 On the boundary value problem for the elliptic system of linear differential equations. Zbl 0272.35034 Kashiwara, M.; Kawai, T. 2 1973 Structure of cohomology groups whose coefficients are microfunction solution sheaves of systems of pseudo-differential equations with multiple characteristics. II. Zbl 0307.35082 Kashiwara, Masaki; Kawai, Takahiro; Oshima, Toshio 2 1974 On the structure of Painlevé transcendents with a large parameter. Zbl 0794.34049 Kawai, Takahiro; Takei, Yoshitsugu 2 1993 Local extension of solutions of systems of linear differential equations with constant coefficients. Zbl 0344.35065 Bedford, Eric; Kawai, Takahiro 2 1977 Theory of elliptic boundary value problems and its applications. Zbl 0376.35022 Kashiwara, Masaki; Kawai, Takahiro 2 1975 Vanishing of cohomology groups on completely k-convex sets. Zbl 0369.32007 Kawai, Takahiro 2 1976 On holonomic systems with regular singularities. Zbl 0425.70017 Kashiwara, Masaki; Kawai, Takahiro 2 1979 Invariance of cohomology groups under a deformation of an elliptic system of linear differential equations. Zbl 0452.58024 Kawai, Takahiro 2 1977 On holonomic systems with regular singularities. Zbl 0482.35060 Kashiwara, Masaki; Kawai, Takahiro 2 1978 Systems of linear differential equations of infinite order: An aspect of infinite analysis. Zbl 0694.35225 Kawai, Takahiro 2 1989 Construction of local elementary solutions for linear partial differential operators with real analytic coefficients. II: The case with complex principal symbols. Zbl 0216.12401 Kawai, Takahiro 2 1971 On the global existence of real analytic solutions of linear differential equations. I. Zbl 0223.35020 Kawai, Takahiro 2 1971 Remembering Leon Ehrenpreis (1930–2010). Zbl 1225.01086 Struppa, Daniele C.; Farkas, Hershel; Kawai, Takahiro; Kuchment, Peter; Quinto, Eric Todd; Sternberg, Shlomo; Taylor, Alan 2 2011 Systems of microdifferential equations of infinite order. Zbl 0759.58044 Kawai, Takahiro 1 1986 On the structure of Painlevé transcendents with a large parameter. II. Zbl 0873.34048 Kawai, Takahiro; Takei, Yoshitsugu 1 1996 Interpolation theorems in several complex variables and applications. Zbl 0796.32001 Berenstein, C. A.; Kawai, T.; Struppa, D. C. 1 1993 On the global existence of real analytic solutions of linear differential equations. II. Zbl 0259.35062 Kawai, T. 1 1973 Pearcey system re-examined from the viewpoint of \(s\)-virtual turning points and non-hereditary turning points. Zbl 1460.34110 Hirose, Sampei; Kawai, Takahiro; Takei, Yoshitsugu 1 2019 On the singularity structure of WKB solution of the boosted Whittaker equation: its relevance to resurgent functions with essential singularities. Zbl 1372.34140 Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya 1 2016 Virtual turning points. Zbl 1354.34003 Honda, Naofumi; Kawai, Takahiro; Takei, Yoshitsugu 23 2015 Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point. I: Its WKB-theoretic transformation to the Mathieu equation. Zbl 1293.35300 Kamimoto, Shingo; Kawai, Takahiro; Takei, Yoshitsugu 8 2014 Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point. II: Its relevance to the Mathieu equation and the Legendre equation. Zbl 1293.35301 Kamimoto, Shingo; Kawai, Takahiro; Takei, Yoshitsugu 7 2014 On the geometric aspect of Sato’s postulates on the \(S\)-matrix. Zbl 1328.81118 Honda, Naofumi; Kawai, Takahiro; Stapp, Henry P. 1 2014 Resurgent functions and linear differential operators of infinite order – Their happy marriage in exact WKB analysis. Zbl 1329.34142 Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya 1 2014 Microlocal analysis of fixed singularities of WKB solutions of a Schrödinger equation with a merging triplet of two simple poles and a simple turning point. Zbl 1279.34105 Kamimoto, Shingo; Kawai, Takahiro; Takei, Yoshitsugu 3 2012 WKB analysis of higher order Painlevé equations with a large parameter. II. Structure theorem for instanton-type solutions of \((P_J)_m (J= I, 34\), II-2 or IV) near a simple \(P\)-turning point of the first kind. Zbl 1228.34144 Kawai, Takahiro; Takei, Yoshitsugu 3 2011 On the exact WKB analysis of higher order simple-pole type operators. Zbl 1231.34155 Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu 3 2011 Remembering Leon Ehrenpreis (1930–2010). Zbl 1225.01086 Struppa, Daniele C.; Farkas, Hershel; Kawai, Takahiro; Kuchment, Peter; Quinto, Eric Todd; Sternberg, Shlomo; Taylor, Alan 2 2011 On a Schrödinger equation with a merging pair of simple pole and a simple turning point – alien calculus of WKB solutions through microlocal analysis. Zbl 1251.34103 Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu 1 2011 On the WKB-theoretic structure of a Schrödinger operator with a merging pair of a simple pole and a simple turning point. Zbl 1201.34141 Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu 8 2010 On the structure of higher order simple-pole type operators in exact WKB analysis. Zbl 1218.34105 Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu 1 2010 The Bender-Wu analysis and the Voros theory. II. Zbl 1175.34112 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 20 2009 Half of the Toulose project Part 5 is completed – structure theorem for instanton-type solutions of \((P_j)_m(J=\text{ I, II or IV})\) near a simple \(P\)-turning point of the first kind. Zbl 1144.34059 Kawai, Takahiro; Takei, Yoshitsugu 1 2008 Virtual turning points – a gift of microlocal analysis to the exact WKB analysis. Zbl 1145.34383 Aoki, Takashi; Honda, Naofumi; Kawai, Takahiro; Koike, Tatsuya; Nishikawa, Yukihiro; Sasaki, Shunsuke; Shudo, Akira; Takei, Yoshitsugu 3 2007 WKB analysis of higher order Painlevé equations with a large parameter – local reduction of 0-parameter solutions for Painlevé hierarchies \((P_{J})\) (\(J=\text{ I, II-1 or II-2}\)). Zbl 1108.34065 Kawai, Takahiro; Takei, Yoshitsugu 6 2006 Algebraic analysis of singular perturbation theory. Transl. from the Japanese by Goro Kato. Zbl 1100.34004 Kawai, Takahiro; Takei, Yoshitsugu 76 2005 Virtual turning points and bifurcation of Stokes curves for higher order ordinary differential equations. Zbl 1073.34098 Aoki, Takashi; Kawai, Takahiro; Sasaki, Shunsuke; Shudo, Akira; Takei, Yoshitsugu 12 2005 On global aspects of exact WKB analysis of operators admitting infinitely many phases. Zbl 1087.34064 Aoki, Takashi; Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu 1 2005 On the Stokes geometry of higher order Painlevé equations. Zbl 1086.34072 Kawai, Takahiro; Koike, Tatsuya; Nishikawa, Yukihiro; Takei, Yoshitsugu 16 2004 On the exact WKB analysis of operators admitting infinitely many phases. Zbl 1056.34103 Aoki, Takashi; Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu 13 2004 On the exact WKB analysis of microdifferential operators of WKB type. Zbl 1079.34070 Aoki, Takashi; Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu 5 2004 The exact steepest descent method – a new steepest descent method based on the exact WKB analysis. Zbl 1072.34105 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 3 2004 On WKB analysis of higher order Painlevé equations with a large parameter. Zbl 1067.34088 Kawai, Takahiro; Takei, Yoshitsugu 1 2004 Exact WKB analysis of non-adiabatic transition probabilities for three levels. Zbl 1027.81010 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 6 2002 On infra-red singularities associated with \(QC\) photons. Zbl 1070.81529 Kawai, Takahiro; Stapp, Henry P. 1 2002 Microlocal analysis and complex Fourier analysis. Zbl 1021.00004 1 2002 On the exact steepest descent method: a new method for the description of Stokes curves. Zbl 1063.34047 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 7 2001 Overconvergence phenomena and grouping in exponential representation of solutions of linear differential equations of infinite order. Zbl 0984.30003 Kawai, Takahiro; Struppa, Daniele C. 5 2001 Toward the exact WKB analysis of differential equations, linear or non-linear. Papers from the symposium on algebraic analysis of singular perturbations, Kyoto, Japan, November 30–December 5, 1998. Zbl 0969.00055 1 2000 WKB analysis of Painlevé transcendents with a large parameter. III: Local reduction of 2-parameter Painlevé transcendents. Zbl 0901.34057 Kawai, Takahiro; Takei, Yoshitsugu 15 1998 On the exact WKB analysis for the third order ordinary differential equations with a large parameter. Zbl 0963.34045 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 8 1998 Preface to: Mikio Sato. A great Japanese mathematician of the twentieth century. Zbl 0958.01021 Kashiwara, Masaki; Kawai, Takahiro; Yau, Shing-Tung 1 1998 Can we find a new deformation of \((\text{SL}_J)\)? Conjectures and supporting evidences. Zbl 0940.34072 Kawai, Takahiro; Takei, Yoshitsugu 1 1997 Some problems in algebraic analysis of singular perturbations. Zbl 0938.34532 Kawai, Takahiro; Takei, Yoshitsugu 1 1997 WKB analysis of Painlevé transcendents with a large parameter. I. Zbl 0848.34005 Kawai, Takahiro; Takei, Yoshitsugu 16 1996 WKB analysis of Painlevé transcendents with a large parameter. II: Multiple-scale analysis of Painlevé transcendents. Zbl 0894.34050 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 15 1996 Interpolating varieties and the Fabry-Ehrenpreis-Kawai gap theorem. Zbl 0890.32007 Berenstein, C. A.; Kawai, T.; Struppa, D. C. 7 1996 Exponential representation of a holomorphic solution of a system of differential equations associated with the theta-zerovalue. Zbl 0973.35055 Berenstein, Carlos A.; Kawai, Takahiro; Struppa, Daniele C.; Takei, Yoshitsugu 2 1996 On the structure of Painlevé transcendents with a large parameter. II. Zbl 0873.34048 Kawai, Takahiro; Takei, Yoshitsugu 1 1996 New turning points in the exact WKB analysis for higher-order ordinary differential equations. Zbl 0831.34058 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 21 1994 Secular equations through the exact WKB analysis. Zbl 0834.34068 Kawai, Takahiro; Takei, Yoshitsugu 5 1994 Algebraic analysis of singular perturbations – on exact WKB analysis. Zbl 0871.32015 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 10 1993 Infrared catastrophe in a massless Feynman function. Zbl 0809.46088 Kawai, T.; Stapp, H. P. 3 1993 On the structure of Painlevé transcendents with a large parameter. Zbl 0794.34049 Kawai, Takahiro; Takei, Yoshitsugu 2 1993 Interpolation theorems in several complex variables and applications. Zbl 0796.32001 Berenstein, C. A.; Kawai, T.; Struppa, D. C. 1 1993 WKB analysis, period integrals, deformations, \(\ldots\). Zbl 0966.34502 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 1 1992 The Bender-Wu analysis and the Voros theory. Zbl 0782.35060 Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu 31 1991 The structure of cohomology groups associated with the theta-zerovalues. Zbl 1138.32300 Kashiwara, Masaki; Kawai, Takahiro; Takei, Yoshitsugu 1 1991 On the existence of holomorphic solutions of systems of linear differential equations of infinite order and with constant coefficients. Zbl 0704.35015 Kawai, Takahiro; Struppa, Daniele C. 6 1990 Bicharacteristical convexity and the semi-global existence of holomorphic solutions of linear differential equations with holomorphic coefficients. Zbl 0703.35003 Kawai, Takahiro; Takei, Yoshitsugu 1 1990 On the boundary value of a solution of the heat equation. Zbl 0696.35066 Kawai, Takahiro; Matsuzawa, Tadato 3 1989 Systems of linear differential equations of infinite order: An aspect of infinite analysis. Zbl 0694.35225 Kawai, Takahiro 2 1989 Microlocal analysis of infrared singularities. Zbl 0701.46058 Kawai, Takahiro; Stapp, Henry P. 1 1989 A particular partition of unity: An auxiliary tool in Hodge theory. Zbl 0702.14005 Kashiwara, Masaki; Kawai, Takahiro 1 1989 The Poincaré lemma for variations of polarized Hodge structure. Zbl 0629.14005 Kashiwara, Masaki; Kawai, Takahiro 31 1987 The Fabry-Ehrenpreis gap theorem and linear differential equations of infinite order. Zbl 0618.30003 Kawai, Takahiro 8 1987 Foundations of algebraic analysis. Transl. from the Japanese by Goro Kato. Zbl 0605.35001 Kashiwara, Masaki; Kawai, Takahiro; Kimura, Tatsuo 47 1986 Hodge structure and holonomic systems. Zbl 0629.14006 Kashiwara, Masaki; Kawai, Takahiro 9 1986 On a class of linear differential operators of infinite order with finite index. Zbl 0628.35003 Aoki, Takashi; Kashiwara, Masaki; Kawai, Takahiro 7 1986 Systems of microdifferential equations of infinite order. Zbl 0759.58044 Kawai, Takahiro 1 1986 On a closed range property of a linear differential operator. Zbl 0607.35033 Kawai, Takahiro; Takei, Yoshitsugu 1 1986 On the global existence of real analytic solutions and hyperfunction solutions of linear differential equations. Zbl 0618.35002 Kawai, Takahiro 1 1986 The Poincaré lemma for a variation of polarized Hodge structure. Zbl 0576.14010 Kashiwara, Masaki; Kawai, Takahiro 4 1985 Microlocal analysis of theta functions. Zbl 0603.10023 Sato, Mikio; Kashiwara, Masaki; Kawai, Takahiro 7 1984 The Fabry-Ehrenpreis gap theorem for hyperfunctions. Zbl 0554.46017 Kawai, Takahiro 2 1984 Linear Differential equations of infinite order and theta functions. Zbl 0546.35047 Sato, Mikio; Kashiwara, Masaki; Kawai, Takahiro 8 1983 Microlocal analysis. Zbl 0536.58030 Kashiwara, Masaki; Kawai, Takahiro 6 1983 An example of a complex of linear differential operators of infinite order. Zbl 0525.35082 Kawai, Takahiro 2 1983 On the regular holonomic character of the S-matrix and microlocal analysis of unitarity-type integrals. Zbl 0491.35066 Kawai, Takahiro; Stapp, Henry P. 5 1982 Poisson’s summation formula and Hamburger’s theorem. Zbl 0499.10042 Ehrenpreis, Leon; Kawai, Takahiro 3 1982 On holonomic systems of microdifferential equations. III: Systems with regular singularities. Zbl 0505.58033 Kashiwara, Masaki; Kawai, Takahiro 119 1981 Second-microlocalization and asymptotic expansions. Zbl 0458.46027 Kashiwara, Masaki; Kawai, Takahiro 36 1980 The theory of holonomic systems with regular singularities and its relevance to physical problems. Zbl 0459.70013 Kashiwara, Masaki; Kawai, Takahiro 3 1980 On a class of linear partial differential equations whose formal solutions always converge. Zbl 0411.35003 Kashiwara, Masaki; Kawai, Takahiro; Sjöstrand, Johannes 16 1979 On holonomic systems for \(\prod_{l=1}^N(f_l+\sqrt{-1}0)^{\lambda_l}\). Zbl 0449.35067 Kashiwara, Masaki; Kawai, Takahiro 15 1979 On the characteristic variety of a holonomic system with regular singularities. Zbl 0449.58019 Kashiwara, Masaki; Kawai, Takahiro 13 1979 Seminar on micro-local analysis. Zbl 0409.00007 Guillemin, Victor W.; Kashiwara, Masaki; Kawai, Takahiro 6 1979 Some applications of boundary value problems for elliptic systems of linear differential equations. Zbl 0454.46033 Kashiwara, Masaki; Kawai, Takahiro 6 1979 Micro-local analysis of Feynman amplitudes. Zbl 0454.46034 Kashiwara, Masaki; Kawai, Takahiro 3 1979 Micro-analyticity of the S-matrix and related functions. Zbl 0424.35078 Kashiwara, Masaki; Kawai, Takahiro; Stapp, Henry P. 3 1979 On holonomic systems with regular singularities. Zbl 0425.70017 Kashiwara, Masaki; Kawai, Takahiro 2 1979 Extended Landau variety and the singularity spectrum of position-space Feynman amplitudes. Zbl 0454.46035 Kawai, Takahiro 1 1979 Monodromy structure of solutions of holonomic systems of linear differential equations is invariant under the deformation of the system. Zbl 0475.35005 Kashiwara, Masaki; Kawai, Takahiro 1 1979 A study of Feynman integrals by micro-differential equations. Zbl 0392.46025 Kashiwara, Masaki; Kawai, Takahiro; Oshima, Toshio 8 1978 Microlocal properties of local elementary solutions for Cauchy problems for a class of hyperbolic linear differential operators. Zbl 0389.35032 Kawai, Takahiro; Nakamura, Gen 3 1978 On holonomic systems with regular singularities. Zbl 0482.35060 Kashiwara, Masaki; Kawai, Takahiro 2 1978 Holonomic systems of linear differential equations and Feynman integrals. Zbl 0449.35095 Kashiwara, Masaki; Kawai, Takahiro 16 1977 Discontinuity formula and Sato’s conjecture. Zbl 0368.35067 Kawai, Takahiro; Stapp, Henry P. 7 1977 Micro-analytic structure of the S-matrix and related functions. Zbl 0443.35059 Kashiwara, Masaki; Kawai, Takahiro; Stapp, Henry P. 6 1977 Holonomic character and local monodromy structure of Feynman integrals. Zbl 0367.46039 Kashiwara, Masaki; Kawai, Takahiro 5 1977 Local extension of solutions of systems of linear differential equations with constant coefficients. Zbl 0344.35065 Bedford, Eric; Kawai, Takahiro 2 1977 Invariance of cohomology groups under a deformation of an elliptic system of linear differential equations. Zbl 0452.58024 Kawai, Takahiro 2 1977 Finiteness theorem for holonomic systems of micro-differential equations. Zbl 0361.35064 Kashiwara, Masaki; Kawai, Takahiro 8 1976 On a conjecture of Regge and Sato on Feynman integrals. Zbl 0347.35061 Kashiwara, Masaki; Kawai, Takahiro 6 1976 Extension of solutions of systems of linear differential equations. Zbl 0366.58013 Kawai, Takahiro 5 1976 Vanishing of cohomology groups on completely k-convex sets. Zbl 0369.32007 Kawai, Takahiro 2 1976 Structure of a single pseudodifferential equation in a real domain. Zbl 0318.35076 Kashiwara, M.; Kawai, T.; Oshima, T. 1 1976 ...and 28 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 647 Authors 65 Kawai, Takahiro 52 Kashiwara, Masaki 29 Schapira, Pierre 25 Takei, Yoshitsugu 19 Aoki, Takashi 16 Oaku, Toshinori 16 Saito, Morihiko 11 D’Agnolo, Andrea 11 Iwaki, Kohei 11 Nang, Philibert 11 Okada, Yasunori 11 Oshima, Toshio 11 Tajima, Shinichi 11 Tose, Nobuyuki 10 Monteiro Fernandes, Maria Teresa de Lemos 9 Ishimura, Ryuichi 9 Laurent, Yves 9 Struppa, Daniele Carlo 9 Yoshino, Masafumi 8 Koike, Tatsuya 8 Pilipović, Stevan 8 Takeuchi, Kiyoshi 8 Uchida, Motoo 8 Zampieri, Giuseppe 7 Kaneko, Akira 7 Kobayashi, Toshiyuki 7 Sjöstrand, Johannes 7 Stapp, Henry P. 7 Ünsal, Mithat 6 Brylinski, Jean-Luc 6 Langenbruch, Michael 6 Takayama, Nobuki 5 Andronikof, Emmanuel 5 Honda, Naofumi 5 Lebeau, Gilles 5 Liess, Otto 5 Nagamachi, Shigeaki 5 Neitzke, Andrew 5 Neto, Orlando 5 Sabbah, Claude 5 Sato, Mikio 4 Abanin, Aleksandr Vasil’evich 4 Berenstein, Carlos Alberto 4 Budur, Nero 4 Chung, Soon-Yeong 4 Debrouwere, Andreas 4 Enomoto, Seishi 4 Ginzburg, Victor 4 Ito, Katsushi 4 Kamimoto, Shingo 4 Kim, Dohan 4 Kudryashov, Nikolaĭ Alekseevich 4 Lê Hai Khôi 4 Malek, Stéphane 4 Malgrange, Bernard 4 Matsuda, Tomohiro 4 Pham, Frédéric 4 Quinto, Eric Todd 4 Uchikoshi, Keisuke 4 Vilonen, Kari 4 Wakabayashi, Seiichiro 4 Walther, Uli 3 Bengel, Gunter 3 Bertola, Marco 3 Boutet de Monvel, Louis 3 de Cataldo, Mark Andrea A. 3 Gaiotto, Davide 3 Gordoa, Pilar Ruiz 3 Guillemin, Victor W. 3 Guillermou, Stéphane 3 Hollands, Lotte 3 Iagolnitzer, Daniel 3 Klausen, René Pascal 3 Klimeš, Martin 3 Komijani, Javad 3 Kruse, Karsten 3 Li, Baoqin 3 Masoero, Davide 3 Migliorini, Luca 3 Miwa, Tetsuji 3 Morimoto, Mitsuo 3 Mugibayashi, Nobumichi 3 Muro, Masakazu 3 Nguyen Tien-Dai 3 Oberst, Ulrich 3 Petit, François 3 Pickering, Andrew 3 Quadrat, Alban 3 Ramis, Jean-Pierre 3 Sekiguchi, Jiro 3 Shapiro, Boris Zalmanovich 3 Shu, Hongfei 3 Sulejmanpasic, tin 3 Suwa, Tatsuo 3 Takahashi, Toshinori 3 Uchida, Shofu 3 Umeta, Yoko 3 van der Veer, Robin 3 Wu, Jingxiang 3 Wu, Lei ...and 547 more Authors all top 5 Cited in 148 Serials 96 Publications of the Research Institute for Mathematical Sciences, Kyoto University 59 Proceedings of the Japan Academy. Series A 35 Advances in Mathematics 33 Journal of High Energy Physics 29 Inventiones Mathematicae 29 Proceedings of the Japan Academy 27 Annales de l’Institut Fourier 25 Communications in Mathematical Physics 24 Duke Mathematical Journal 19 Bulletin de la Société Mathématique de France 15 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 14 Compositio Mathematica 12 Transactions of the American Mathematical Society 11 Letters in Mathematical Physics 11 Communications in Partial Differential Equations 11 Journal of Physics A: Mathematical and Theoretical 10 Journal of Differential Equations 10 Journal of Functional Analysis 8 Arkiv för Matematik 8 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 8 Mathematische Annalen 8 Tôhoku Mathematical Journal. Second Series 8 Selecta Mathematica. New Series 7 Proceedings of the American Mathematical Society 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Journal of Mathematical Analysis and Applications 6 Journal of the Mathematical Society of Japan 6 Journal of Pure and Applied Algebra 5 Journal d’Analyse Mathématique 5 Mathematische Zeitschrift 5 Nagoya Mathematical Journal 5 Rendiconti del Seminario Matematico della Università di Padova 5 Journal of Algebraic Geometry 5 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 4 Communications on Pure and Applied Mathematics 4 Acta Mathematica 4 Mathematische Nachrichten 4 The Journal of Geometric Analysis 4 Mémoires de la Société Mathématique de France. Nouvelle Série 4 Bulletin des Sciences Mathématiques 4 Annales Henri Poincaré 4 Bulletin of the American Mathematical Society 3 Journal of Mathematical Physics 3 Studies in Applied Mathematics 3 Constructive Approximation 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Bulletin of the American Mathematical Society. New Series 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Regular and Chaotic Dynamics 3 Complex Variables and Elliptic Equations 2 Computer Physics Communications 2 Nuclear Physics. B 2 Reports on Mathematical Physics 2 Rocky Mountain Journal of Mathematics 2 Theoretical and Mathematical Physics 2 Journal of Geometry and Physics 2 Beiträge zur Algebra und Geometrie 2 Applied Mathematics and Computation 2 Functiones et Approximatio. Commentarii Mathematici 2 Funkcialaj Ekvacioj. Serio Internacia 2 Journal of Algebra 2 Journal of Differential Geometry 2 Journal für die Reine und Angewandte Mathematik 2 Manuscripta Mathematica 2 Tsukuba Journal of Mathematics 2 Journal of Symbolic Computation 2 International Journal of Mathematics 2 Journal of Mathematical Sciences (New York) 2 Advances in Applied Clifford Algebras 2 Integral Transforms and Special Functions 2 The Journal of Fourier Analysis and Applications 2 Abstract and Applied Analysis 2 Mathematical Physics, Analysis and Geometry 2 Annals of Mathematics. Second Series 2 Qualitative Theory of Dynamical Systems 2 Mathematics in Computer Science 2 Complex Analysis and Operator Theory 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Portugaliae Mathematica 2 SciPost Physics 1 International Journal of Modern Physics A 1 Archive for History of Exact Sciences 1 International Journal of Theoretical Physics 1 Israel Journal of Mathematics 1 Physics Reports 1 Studia Mathematica 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Collectanea Mathematica 1 Functional Analysis and its Applications 1 Publications Mathématiques 1 Journal of Approximation Theory 1 Journal of Computational and Applied Mathematics 1 Memoirs of the American Mathematical Society 1 Monatshefte für Mathematik 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Results in Mathematics 1 SIAM Journal on Control and Optimization 1 Siberian Mathematical Journal 1 Tokyo Journal of Mathematics ...and 48 more Serials all top 5 Cited in 55 Fields 281 Partial differential equations (35-XX) 250 Several complex variables and analytic spaces (32-XX) 153 Algebraic geometry (14-XX) 143 Global analysis, analysis on manifolds (58-XX) 115 Ordinary differential equations (34-XX) 113 Functional analysis (46-XX) 104 Quantum theory (81-XX) 47 Differential geometry (53-XX) 41 Operator theory (47-XX) 35 Topological groups, Lie groups (22-XX) 33 Commutative algebra (13-XX) 33 Special functions (33-XX) 27 Functions of a complex variable (30-XX) 20 Dynamical systems and ergodic theory (37-XX) 19 Category theory; homological algebra (18-XX) 19 Integral transforms, operational calculus (44-XX) 18 Associative rings and algebras (16-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 16 Number theory (11-XX) 13 Algebraic topology (55-XX) 11 Nonassociative rings and algebras (17-XX) 11 Computer science (68-XX) 9 Relativity and gravitational theory (83-XX) 8 Systems theory; control (93-XX) 7 Difference and functional equations (39-XX) 7 Abstract harmonic analysis (43-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 Manifolds and cell complexes (57-XX) 5 Group theory and generalizations (20-XX) 5 Sequences, series, summability (40-XX) 5 Approximations and expansions (41-XX) 5 Numerical analysis (65-XX) 4 Mathematical logic and foundations (03-XX) 4 Integral equations (45-XX) 4 Mechanics of particles and systems (70-XX) 3 History and biography (01-XX) 3 Field theory and polynomials (12-XX) 3 Real functions (26-XX) 3 Potential theory (31-XX) 3 Fluid mechanics (76-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 \(K\)-theory (19-XX) 2 Astronomy and astrophysics (85-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Measure and integration (28-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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