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## Sakai, Shoichiro

Compute Distance To:
 Author ID: sakai.shoichiro Published as: Sakai, S.; Sakai, Shoichiro; Sakai, Shôichiro; Sakai, Shôichirô External Links: MGP · Wikidata · GND
 Documents Indexed: 76 Publications since 1952, including 5 Books

#### Co-Authors

 72 single-authored 2 Powers, Robert T. 1 Kishimoto, Akitaka 1 Ozawa, Narutaka 1 Price, Geoffrey L.
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#### Serials

 9 Tohoku Mathematical Journal. Second Series 7 Journal of Functional Analysis 6 Proceedings of the Japan Academy 4 American Journal of Mathematics 3 Proceedings of the American Mathematical Society 3 Bulletin of the American Mathematical Society 2 Communications in Mathematical Physics 2 Pacific Journal of Mathematics 2 RIMS Kokyuroku 2 Encyclopedia of Mathematics and Its Applications 2 Publications of the Research Institute for Mathematical Sciences, Series A 1 Bulletin de la Société Mathématique de France 1 Canadian Mathematical Bulletin 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Transactions of the American Mathematical Society 1 Sūgaku 1 Sugaku Expositions 1 Annals of Mathematics. Second Series 1 Kodai Mathematical Seminar Reports 1 Ergebnisse der Mathematik und ihrer Grenzgebiete 1 Operators and Matrices 1 Classics in Mathematics
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#### Fields

 47 Functional analysis (46-XX) 8 Operator theory (47-XX) 6 Statistical mechanics, structure of matter (82-XX) 3 Topological groups, Lie groups (22-XX) 2 Mathematical logic and foundations (03-XX) 1 General and overarching topics; collections (00-XX) 1 Measure and integration (28-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX)

#### Citations contained in zbMATH Open

54 Publications have been cited 995 times in 816 Documents Cited by Year
$$C^ *$$-algebras and $$W^ *$$-algebras. Zbl 0219.46042
Sakai, S.
1971
Derivations of $$W^ *$$-algebras. Zbl 0139.30601
Sakai, S.
1966
Derivations of simple $$C^ *$$-algebras. III. Zbl 0233.46074
Sakai, Shôichirô
1971
$$C^*$$-algebras and $$W^*$$-algebras. Reprint of the 1971 edition. Zbl 1024.46001
Sakai, Shôichirô
1998
Operator algebras in dynamical systems. The theory of unbounded derivations in $$C^*$$-algebras. Zbl 0743.46078
Sakai, Shôichirô
1991
Weakly compact operators on operator algebras. Zbl 0135.35803
Sakai, S.
1964
On a conjecture of Kaplansky. Zbl 0109.34201
Sakai, S.
1960
A characterization of W*-algebras. Zbl 0072.12404
Sakai, Shoichiro
1956
Existence of ground states and KMS states for approximately inner dynamics. Zbl 0298.46065
Powers, Robert T.; Sakai, Shoichiro
1975
On topological properties of $$W^*$$-algebras. Zbl 0081.11103
Sakai, Shôichirô
1957
Unbounded derivations in operator algebras. Zbl 0337.46048
Powers, Robert T.; Sakai, Shoichiro
1975
A Radon-Nikodym theorem in $$W^ *$$-algebras. Zbl 0132.10803
Sakai, S.
1965
On one-parameter subgroups of $$^*$$-automorphisms on operator algebras and the corresponding unbounded derivations. Zbl 0344.46120
Sakai, Shoichiro
1976
Derivations of simple $$C^ *$$-algebras. Zbl 0172.41104
Sakai, S.
1968
Homogeneity of the pure state space of a separable $$C^{\ast}$$-algebra. Zbl 1066.46052
Kishimoto, Akitaka; Ozawa, Narutaka; Sakai, Shôichirô
2003
On a characterization of type I $$C^ *$$-algebras. Zbl 0141.12305
Sakai, S.
1966
Derivations of simple $$C^*$$-algebras. II. Zbl 0216.41401
Sakai, S.
1971
Automorphisms and tensor products of operator algebras. Zbl 0321.46052
Sakai, Shoichiro
1976
On commutative normal $$^*$$-derivations. Zbl 0312.46073
Sakai, Shoichiro
1975
On the Stone-Weierstrass theorem of $$C^ *$$-algebras. Zbl 0211.16001
Sakai, S.
1970
On linear functionals of $$W^*$$-algebras. Zbl 0084.33602
Sakai, Shôichirô
1958
On commutative normal $$^*$$-derivations. II. Zbl 0345.46048
Sakai, Shoichiro
1976
An uncountable number of $$II^ 1$$ and $$II^ \infty$$ factors. Zbl 0198.17804
Sakai, S.
1970
Asymptotically abelian $$II_ 1$$ factors. Zbl 0195.42103
Sakai, Shoichiro
1968
On the groups isomorphism of unitary groups in $$AW^*$$-algebras. Zbl 0066.36201
Sakai, Shôichirô
1955
On global type II$$_1$$ W$$^*$$-algebras. Zbl 0267.46048
Sakai, S.
1972
On the central decomposition for positive functionals on $$C^ *$$- algebras. Zbl 0135.35901
Sakai, S.
1965
Statistical mechanics and unbounded derivations in C*-algebras. Zbl 0528.46044
Sakai, S.
1984
Recent developments in the theory of unbounded derivations in $$C^*$$- algebras. Zbl 0392.46040
Sakai, Shoichiro
1978
On automorphism groups of $$II_1$$-factors. Zbl 0303.46060
Sakai, Shoichiro
1974
On a problem of Calkin. Zbl 0163.36703
Sakai, S.
1966
Derived C$$^*$$-algebras of primitive C$$^*$$-algebras. Zbl 0266.46046
Sakai, Shoichiro
1973
On type I $$C^*$$-algebras. Zbl 0182.46601
Sakai, S.
1967
Recent developments in the theory of unbounded derivations in C*- algebras. Zbl 0458.46046
Sakai, Shoichiro
1980
Commutative normal $$^*$$-derivations. III. Zbl 0345.46049
Sakai, Shoichiro
1976
On the tensor product of $$W^ *$$-algebras. Zbl 0164.15801
Sakai, S.
1968
Derivations of uniformly hyperfinite $$C^ *$$-algebras. Zbl 0167.43501
Sakai, S.
1967
On some problems of $$C^ *$$-algebras. Zbl 0135.35802
Sakai, S.
1959
The absolute value of $$W^*$$-algebras of finite type. Zbl 0071.11402
Sakai, Shôichirô
1956
On the representations of semi-simple Lie groups. Zbl 0057.34101
Sakai, Shôichiro
1954
Operator algebras in dynamical systems. The theory of unbounded derivations in $$C^*$$-algebras. Paperback reprint of the hardback edition 1991. Zbl 1143.46041
Sakai, Shôichirô
2008
Extremal marginal tracial states in coupled systems. Zbl 1141.46030
Price, Geoffrey L.; Sakai, Shôichirô
2007
Derivations in operator algebras. Zbl 0524.46034
Sakai, Shoichiro
1983
Developments in the theory of unbounded derivations in $$C^*$$-algebras. Zbl 0533.46038
Sakai, Shôichirô
1982
On extensions of mappings into n-cubes. Zbl 0179.27901
Sakai, S.
1968
On the hyperfinite II$$_ 1$$-factor. Zbl 0157.44604
Sakai, S.
1968
On topologies of finite $$W^ *$$-algebras. Zbl 0135.35805
Sakai, S.
1965
On the reduction theory of von Neumann. Zbl 0135.35804
Sakai, S.
1964
On the $$\sigma$$-weak topology of $$W^*$$-algebras. Zbl 0071.11401
Sakai, Shôichirô
1956
Pure states on $$C^*$$-algebras. Zbl 1049.46046
Sakai, Shôichirô
2003
Perturbations and KMS states in C *-dynamical systems (generalization of the absence theorem of phase transition to continuous quantum systems). Zbl 0638.46048
Sakai, Shôichirô
1987
Phase transition free states on UHF algebras. Zbl 0513.46039
Sakai, Shoichiro
1982
On global type $$II_ 1 W^ *$$ algebras. Zbl 0221.46059
Sakai, Shôichirô
1971
On global $$W^ *$$-algebras. Zbl 0167.43502
Sakai, S.
1969
Operator algebras in dynamical systems. The theory of unbounded derivations in $$C^*$$-algebras. Paperback reprint of the hardback edition 1991. Zbl 1143.46041
Sakai, Shôichirô
2008
Extremal marginal tracial states in coupled systems. Zbl 1141.46030
Price, Geoffrey L.; Sakai, Shôichirô
2007
Homogeneity of the pure state space of a separable $$C^{\ast}$$-algebra. Zbl 1066.46052
Kishimoto, Akitaka; Ozawa, Narutaka; Sakai, Shôichirô
2003
Pure states on $$C^*$$-algebras. Zbl 1049.46046
Sakai, Shôichirô
2003
$$C^*$$-algebras and $$W^*$$-algebras. Reprint of the 1971 edition. Zbl 1024.46001
Sakai, Shôichirô
1998
Operator algebras in dynamical systems. The theory of unbounded derivations in $$C^*$$-algebras. Zbl 0743.46078
Sakai, Shôichirô
1991
Perturbations and KMS states in C *-dynamical systems (generalization of the absence theorem of phase transition to continuous quantum systems). Zbl 0638.46048
Sakai, Shôichirô
1987
Statistical mechanics and unbounded derivations in C*-algebras. Zbl 0528.46044
Sakai, S.
1984
Derivations in operator algebras. Zbl 0524.46034
Sakai, Shoichiro
1983
Developments in the theory of unbounded derivations in $$C^*$$-algebras. Zbl 0533.46038
Sakai, Shôichirô
1982
Phase transition free states on UHF algebras. Zbl 0513.46039
Sakai, Shoichiro
1982
Recent developments in the theory of unbounded derivations in C*- algebras. Zbl 0458.46046
Sakai, Shoichiro
1980
Recent developments in the theory of unbounded derivations in $$C^*$$- algebras. Zbl 0392.46040
Sakai, Shoichiro
1978
On one-parameter subgroups of $$^*$$-automorphisms on operator algebras and the corresponding unbounded derivations. Zbl 0344.46120
Sakai, Shoichiro
1976
Automorphisms and tensor products of operator algebras. Zbl 0321.46052
Sakai, Shoichiro
1976
On commutative normal $$^*$$-derivations. II. Zbl 0345.46048
Sakai, Shoichiro
1976
Commutative normal $$^*$$-derivations. III. Zbl 0345.46049
Sakai, Shoichiro
1976
Existence of ground states and KMS states for approximately inner dynamics. Zbl 0298.46065
Powers, Robert T.; Sakai, Shoichiro
1975
Unbounded derivations in operator algebras. Zbl 0337.46048
Powers, Robert T.; Sakai, Shoichiro
1975
On commutative normal $$^*$$-derivations. Zbl 0312.46073
Sakai, Shoichiro
1975
On automorphism groups of $$II_1$$-factors. Zbl 0303.46060
Sakai, Shoichiro
1974
Derived C$$^*$$-algebras of primitive C$$^*$$-algebras. Zbl 0266.46046
Sakai, Shoichiro
1973
On global type II$$_1$$ W$$^*$$-algebras. Zbl 0267.46048
Sakai, S.
1972
$$C^ *$$-algebras and $$W^ *$$-algebras. Zbl 0219.46042
Sakai, S.
1971
Derivations of simple $$C^ *$$-algebras. III. Zbl 0233.46074
Sakai, Shôichirô
1971
Derivations of simple $$C^*$$-algebras. II. Zbl 0216.41401
Sakai, S.
1971
On global type $$II_ 1 W^ *$$ algebras. Zbl 0221.46059
Sakai, Shôichirô
1971
On the Stone-Weierstrass theorem of $$C^ *$$-algebras. Zbl 0211.16001
Sakai, S.
1970
An uncountable number of $$II^ 1$$ and $$II^ \infty$$ factors. Zbl 0198.17804
Sakai, S.
1970
On global $$W^ *$$-algebras. Zbl 0167.43502
Sakai, S.
1969
Derivations of simple $$C^ *$$-algebras. Zbl 0172.41104
Sakai, S.
1968
Asymptotically abelian $$II_ 1$$ factors. Zbl 0195.42103
Sakai, Shoichiro
1968
On the tensor product of $$W^ *$$-algebras. Zbl 0164.15801
Sakai, S.
1968
On extensions of mappings into n-cubes. Zbl 0179.27901
Sakai, S.
1968
On the hyperfinite II$$_ 1$$-factor. Zbl 0157.44604
Sakai, S.
1968
On type I $$C^*$$-algebras. Zbl 0182.46601
Sakai, S.
1967
Derivations of uniformly hyperfinite $$C^ *$$-algebras. Zbl 0167.43501
Sakai, S.
1967
Derivations of $$W^ *$$-algebras. Zbl 0139.30601
Sakai, S.
1966
On a characterization of type I $$C^ *$$-algebras. Zbl 0141.12305
Sakai, S.
1966
On a problem of Calkin. Zbl 0163.36703
Sakai, S.
1966
A Radon-Nikodym theorem in $$W^ *$$-algebras. Zbl 0132.10803
Sakai, S.
1965
On the central decomposition for positive functionals on $$C^ *$$- algebras. Zbl 0135.35901
Sakai, S.
1965
On topologies of finite $$W^ *$$-algebras. Zbl 0135.35805
Sakai, S.
1965
Weakly compact operators on operator algebras. Zbl 0135.35803
Sakai, S.
1964
On the reduction theory of von Neumann. Zbl 0135.35804
Sakai, S.
1964
On a conjecture of Kaplansky. Zbl 0109.34201
Sakai, S.
1960
On some problems of $$C^ *$$-algebras. Zbl 0135.35802
Sakai, S.
1959
On linear functionals of $$W^*$$-algebras. Zbl 0084.33602
Sakai, Shôichirô
1958
On topological properties of $$W^*$$-algebras. Zbl 0081.11103
Sakai, Shôichirô
1957
A characterization of W*-algebras. Zbl 0072.12404
Sakai, Shoichiro
1956
The absolute value of $$W^*$$-algebras of finite type. Zbl 0071.11402
Sakai, Shôichirô
1956
On the $$\sigma$$-weak topology of $$W^*$$-algebras. Zbl 0071.11401
Sakai, Shôichirô
1956
On the groups isomorphism of unitary groups in $$AW^*$$-algebras. Zbl 0066.36201
Sakai, Shôichirô
1955
On the representations of semi-simple Lie groups. Zbl 0057.34101
Sakai, Shôichiro
1954
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#### Cited by 738 Authors

 26 Peralta, Antonio M. 24 Sakai, Shoichiro 20 Jørgensen, Palle E. T. 19 Kishimoto, Akitaka 15 Ayupov, Shavkat Abdullaevich 12 Bratteli, Ola 12 Edwards, Christopher Martin 12 Lau, Anthony To-Ming 11 Sukochev, Fedor Anatol’evich 11 Tomiyama, Jun 10 Akemann, Charles A. 10 Buchholz, Detlev 10 Elliott, George A. 10 Kudaybergenov, Karimbergen K. 9 Ber, Aleksey Feliksovich 9 Kadison, Richard Vincent 8 Christensen, Erik 8 Rüttimann, Gottfried T. 8 Smith, Roger R. 8 Takesaki, Masamichi 7 Batty, Charles J. K. 7 Fernández-Polo, Francisco J. 7 Garcés, Jorge José 7 Haagerup, Uffe Valentin 6 Araki, Huzihiro 6 Rodríguez Palacios, Angel 6 Wright, John David Maitland 5 Accardi, Luigi 5 Barchielli, Alberto 5 Beltiţă, Daniel 5 Chilin, Vladimir Ivanovich 5 Inoue, Atsushi 5 Kissin, Edward V. 5 Mehdipour, Mohammad Javad 5 Ôta, Schôichi 5 Pedersen, Gert Kjærgård 5 Popa, Sorin Teodor 5 Robinson, Derek W. 5 Weaver, Nik 4 Archbold, Robert J. 4 Evans, David E. 4 Feintzeig, Benjamin H. 4 Fidaleo, Francesco 4 Granirer, Edmond E. 4 Hamana, Masamichi 4 Herman, Richard H. 4 Kirchberg, Eberhard 4 Longo, Roberto 4 Molnár, Lajos 4 Nasr-Isfahani, Rasoul 4 Okayasu, Takateru 4 Paschke, William Lindall 4 Pop, Florin 4 Rieffel, Marc A. 4 Ringrose, John R. 4 Russo, Bernard 4 Shultz, Frederic W. 4 Sinclair, Allan M. 4 Takemoto, Hideo 4 Wassermann, Simon 4 Zanin, Dmitriy V. 4 Zsidó, Lászlo 3 Arzikulov, Farhodjon Nematjonovich 3 Borchers, Hans-Jürgen 3 Brüning, Jochen 3 Bunce, John Winston 3 Ching, Wai-Mee 3 Chu, Choho 3 Dang Ngoc Nghiem 3 de la Harpe, Pierre 3 Effros, Edward George 3 Essaleh, Ahlem Ben Ali 3 Fragoulopoulou, Maria 3 Fredenhagen, Klaus 3 Ghahramani, Fereidoun 3 Hatori, Osamu 3 Iochum, Bruno 3 Junge, Marius 3 Kucerovsky, Dan Z. 3 Lance, E. Christopher 3 Loupias, Guy 3 Marchand, Jean-Paul 3 Medghalchi, Ali Reza 3 Mirzavaziri, Madjid 3 Moslehian, Mohammad Sal 3 Neeb, Karl-Hermann 3 Neufang, Matthias 3 Oikhberg, Timur 3 Peligrad, Costel 3 Razeghi, Mehran 3 Rossi, Stefano 3 Saitô, Kazuyuki 3 Schlichting, Günter 3 Shul’man, Viktor Semënovich 3 Summers, Stephen Jeffrey 3 Vaccaro, Andrea 3 Werner, Reinhard F. 3 Zimmer, Robert J. 2 Aiello, Valeriano 2 Alberti, Peter M. ...and 638 more Authors
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#### Cited in 154 Serials

 113 Journal of Functional Analysis 62 Communications in Mathematical Physics 50 Proceedings of the American Mathematical Society 42 Transactions of the American Mathematical Society 36 Journal of Mathematical Analysis and Applications 33 Tohoku Mathematical Journal. Second Series 23 Mathematische Annalen 22 Reports on Mathematical Physics 20 Inventiones Mathematicae 18 Linear Algebra and its Applications 17 Advances in Mathematics 15 Mathematische Zeitschrift 11 Journal of Algebra 10 International Journal of Theoretical Physics 9 Mathematical Proceedings of the Cambridge Philosophical Society 9 Integral Equations and Operator Theory 9 Publications of the Research Institute for Mathematical Sciences, Kyoto University 8 Bulletin of the American Mathematical Society 7 Journal of Mathematical Physics 7 Acta Mathematica 7 Annales de l’Institut Fourier 7 Journal of Soviet Mathematics 7 Annales de l’Institut Henri Poincaré. Physique Théorique 7 Positivity 7 Proceedings of the Japan Academy 6 Bulletin of the Australian Mathematical Society 6 Linear and Multilinear Algebra 6 Rocky Mountain Journal of Mathematics 5 Reviews in Mathematical Physics 5 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 5 Glasgow Mathematical Journal 5 Manuscripta Mathematica 5 Proceedings of the National Academy of Sciences of the United States of America 5 Lobachevskii Journal of Mathematics 5 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 5 Mediterranean Journal of Mathematics 5 Banach Journal of Mathematical Analysis 5 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Bulletin de la Société Mathématique de France 4 Ergodic Theory and Dynamical Systems 4 Indagationes Mathematicae. New Series 4 Acta Mathematica Sinica. English Series 3 Israel Journal of Mathematics 3 Letters in Mathematical Physics 3 Mathematical Notes 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Functional Analysis and its Applications 3 Fuzzy Sets and Systems 3 Journal of Approximation Theory 3 Journal of Pure and Applied Algebra 3 Mathematische Nachrichten 3 Monatshefte für Mathematik 3 Expositiones Mathematicae 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Communications on Pure and Applied Mathematics 2 Studia Mathematica 2 Theoretical and Mathematical Physics 2 Canadian Journal of Mathematics 2 Compositio Mathematica 2 Duke Mathematical Journal 2 Nagoya Mathematical Journal 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Rendiconti del Seminario Matemàtico e Fisico di Milano 2 Synthese 2 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Topology and its Applications 2 Probability Theory and Related Fields 2 Journal of Theoretical Probability 2 Annales Scientifiques de l’Université Blaise Pascal Clermont-Ferrand II. Mathématiques 2 International Journal of Mathematics 2 Abstract and Applied Analysis 2 Journal of Inequalities and Applications 2 Infinite Dimensional Analysis, Quantum Probability and Related Topics 2 Journal of Dynamical Systems and Geometric Theories 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Bulletin de la Société Mathématique de France. Supplément. Mémoires 2 Publications of the Research Institute for Mathematical Sciences, Series A 2 Transactions of the American Mathematical Society. Series B 2 Advances in Operator Theory 1 International Journal of Modern Physics A 1 Communications in Algebra 1 International Journal of Engineering Science 1 Indian Journal of Pure & Applied Mathematics 1 Nuclear Physics. B 1 Physica A 1 Physics Letters. A 1 Physics Reports 1 Russian Mathematical Surveys 1 Journal of Geometry and Physics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Aplikace Matematiky 1 Archiv der Mathematik 1 Canadian Mathematical Bulletin 1 Czechoslovak Mathematical Journal 1 Dissertationes Mathematicae 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Kodai Mathematical Journal ...and 54 more Serials
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#### Cited in 50 Fields

 619 Functional analysis (46-XX) 215 Operator theory (47-XX) 94 Quantum theory (81-XX) 65 Topological groups, Lie groups (22-XX) 58 Abstract harmonic analysis (43-XX) 40 Nonassociative rings and algebras (17-XX) 34 Associative rings and algebras (16-XX) 31 Probability theory and stochastic processes (60-XX) 30 Statistical mechanics, structure of matter (82-XX) 22 Measure and integration (28-XX) 20 Global analysis, analysis on manifolds (58-XX) 15 Mathematical logic and foundations (03-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 12 Dynamical systems and ergodic theory (37-XX) 10 Group theory and generalizations (20-XX) 10 General topology (54-XX) 9 Category theory; homological algebra (18-XX) 9 Information and communication theory, circuits (94-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 7 Several complex variables and analytic spaces (32-XX) 7 Differential geometry (53-XX) 4 Commutative algebra (13-XX) 4 Algebraic topology (55-XX) 3 Combinatorics (05-XX) 3 Real functions (26-XX) 3 Approximations and expansions (41-XX) 3 Manifolds and cell complexes (57-XX) 3 Statistics (62-XX) 3 Computer science (68-XX) 2 General and overarching topics; collections (00-XX) 2 $$K$$-theory (19-XX) 2 Partial differential equations (35-XX) 2 Difference and functional equations (39-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 2 Systems theory; control (93-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Numerical analysis (65-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

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