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## Shigekawa, Ichiro

Compute Distance To:
 Author ID: shigekawa.ichiro Published as: Shigekawa, I.; Shigekawa, Ichiro; Shigekawa, Ichirō External Links: Wikidata · GND
 Documents Indexed: 53 Publications since 1978, including 3 Books
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#### Co-Authors

 32 single-authored 5 Taniguchi, Setsuo 3 Kazumi, Tetsuya 2 Aida, Shigeki 2 Fukushima, Masatoshi 2 Ueki, Naomasa 1 Elworthy, K. David 1 Ikeda, Nobuyuki 1 Kotani, Shinichi 1 Kusuoka, Seiichiro Kusuoka 1 Kusuoka, Shigeo 1 Manabe, Shojiro 1 Masuda, Takao 1 Matsumoto, Hiroyuki 1 Miyokawa, Tomohiro 1 Watanabe, Shinzo 1 Yoshida, Nobuo 1 Yun, Yong Sik
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#### Serials

 7 Journal of Functional Analysis 5 Osaka Journal of Mathematics 4 Journal of Mathematics of Kyoto University 3 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Probability Theory and Related Fields 2 Sūgaku 2 Kyoto Journal of Mathematics 1 Journal of the Mathematical Society of Japan 1 Mathematical Journal of Okayama University 1 Proceedings of the Japan Academy. Series A 1 Acta Applicandae Mathematicae 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Far East Journal of Mathematical Sciences 1 Translations of Mathematical Monographs 1 Frontiers of Mathematics in China 1 RIMS Kôkyûroku Bessatsu 1 Communications on Stochastic Analysis
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#### Fields

 43 Probability theory and stochastic processes (60-XX) 19 Global analysis, analysis on manifolds (58-XX) 14 Operator theory (47-XX) 6 Functional analysis (46-XX) 5 Partial differential equations (35-XX) 5 Differential geometry (53-XX) 4 Potential theory (31-XX) 2 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral transforms, operational calculus (44-XX) 1 Statistical mechanics, structure of matter (82-XX)

#### Citations contained in zbMATH Open

43 Publications have been cited 437 times in 357 Documents Cited by Year
Derivatives of Wiener functionals and absolute continuity of induced measures. Zbl 0476.28008
Shigekawa, Ichiro
1980
Logarithmic Sobolev inequalities and exponential integrability. Zbl 0846.46020
Aida, Shigeki; Masuda, Takao; Shigekawa, Ichiro
1994
Eigenvalue problems for the Schrödinger operator with the magnetic field on a compact Riemann manifold. Zbl 0629.58023
Shigekawa, Ichiro
1987
De Rham-Hodge-Kodaira’s decomposition on an abstract Wiener space. Zbl 0611.58006
Shigekawa, Ichiro
1986
Stochastic analysis. Translated from the Japanese by Ichiro Shigekawa. Zbl 1064.60003
Shigekawa, Ichiro
2004
Spectral properties of Schrödinger operators with magnetic fields for a spin $${1 \over{} 2}$$ particle. Zbl 0742.47002
Shigekawa, Ichiro
1991
Sobolev spaces over the Wiener space based on an Ornstein-Uhlenbeck operator. Zbl 0777.60047
Shigekawa, Ichiro
1992
Logarithmic Sobolev inequalities and spectral gaps: Perturbation theory. Zbl 0846.46019
Aida, Shigeki; Shigekawa, Ichiro
1994
Transformations of the Brownian motion on a Riemannian symmetric space. Zbl 0518.60087
Shigekawa, Ichiro
1984
Sobolev spaces of Banach-valued functions associated with a Markov process. Zbl 0801.60044
Shigekawa, Ichiro
1994
Existence of invariant measures of diffusions on an abstract Wiener space. Zbl 0636.60080
Shigekawa, Ichiro
1987
On stochastic horizontal lifts. Zbl 0487.60056
Shigekawa, Ichiro
1982
Measures of finite $$(r,p)$$-energy and potentials on a separable metric space. Zbl 0769.60069
Kazumi, Tetsuya; Shigekawa, Ichiro
1992
Itô-Wiener expansions of holomorphic functions on the complex Wiener space. Zbl 0727.60053
Shigekawa, Ichiro
1991
$$L^ p$$ contraction semigroups for vector valued functions. Zbl 0886.47024
Shigekawa, Ichiro
1997
Absolute continuity of probability laws of Wiener functionals. Zbl 0422.60032
Shigekawa, Ichiro
1978
A Kähler metric on a based loop group and a covariant differentiation. Zbl 0867.53029
Shigekawa, Ichiro; Taniguchi, Setsuo
1996
On a quasi everywhere existence of the local time of the 1-dimensional Brownian motion. Zbl 0551.60076
Shigekawa, Ichiro
1984
Vanishing theorem of the Hodge-Kodaira operator for differential forms on a convex domain of the Wiener space. Zbl 1077.58022
Shigekawa, Ichiro
2003
Semigroup domination on a Riemannian manifold with boundary. Zbl 0992.60081
Shigekawa, Ichiro
2000
An example of regular $$(r,p)$$-capacity and essential self-adjointness of a diffusion operator in infinite dimensions. Zbl 0855.31005
Shigekawa, Ichiro
1995
Littlewood-Paley-Stein inequality for a symmetric diffusion. Zbl 0764.60060
Shigekawa, Ichiro; Yoshida, Nobuo
1992
The Meyer inequality for the Ornstein-Uhlenbeck operator in $$L^1$$ and probabilistic proof of Stein’s $$L^p$$ multiplier theorem. Zbl 1010.60051
Shigekawa, Ichiro
1997
Differential calculus on a submanifold of an abstract Wiener space. II: Weitzenböck formula. Zbl 0836.60064
Kazumi, Tetsuya; Shigekawa, Ichiro
1995
A quasihomeomorphism on the Wiener space. Zbl 0821.60059
Shigekawa, Ichiro
1995
The Malliavin calculus and long time asymptotics of certain Wiener integrals. Zbl 0573.60055
Ikeda, Nobuyuki; Shigekawa, Ichiro; Taniguchi, Setsuo
1985
Transformations of the Brownian motion on the Lie group. Zbl 0563.58035
Shigekawa, Ichiro
1984
Defective intertwining property and generator domain. Zbl 1113.47028
Shigekawa, Ichiro
2006
On equivalence of $$L^{p}$$-norms related to Schrödinger type operators on Riemannian manifolds. Zbl 1094.53034
Miyokawa, Tomohiro; Shigekawa, Ichiro
2006
Littlewood-Paley inequality for a diffusion satisfying the logarithmic Sobolev inequality and for the Brownian motion on a Riemannian manifold with boundary. Zbl 1016.58022
Shigekawa, Ichiro
2002
Differential calculus on a submanifold of an abstract Wiener space. I: Covariant derivative. Zbl 0829.46031
Kazumi, T.; Shigekawa, I.
1994
Dirichlet forms on separable metric spaces. Zbl 0818.60068
Shigekawa, Ichiro; Taniguchi, Setsuo
1992
Limit theorems for stochastic flows of diffeomorphisms of jump type. Zbl 0548.60035
Matsumoto, Hiroyuki; Shigekawa, I.
1985
Exponential convergence of Markovian semigroups and their spectra on $$L^p$$-spaces. Zbl 1306.60107
Kusuoka, Seiichiro; Shigekawa, Ichiro
2014
Non-symmetric diffusions on a Riemannian manifold. Zbl 1200.58024
Shigekawa, Ichiro
2010
Orlicz norm equivalence for the Ornstein-Uhlenbeck operator. Zbl 1063.60083
Shigekawa, Ichiro
2004
A probabilistic proof of the Gauss-Bonnet-Chern theorem for manifolds with boundary. Zbl 0704.58056
Shigekawa, Ichiro; Ueki, Naomasa; Watanabe, Shinzo
1989
A stochastic approach to the Riemann-Roch theorem. Zbl 0709.58036
Shigekawa, Ichiro; Ueki, Naomasa
1988
Dual ultracontractivity and its applications. Zbl 1322.47040
Shigekawa, Ichiro
2014
Schrödinger operators on the Wiener space. Zbl 1328.60157
Shigekawa, Ichiro
2007
$$L^p$$ multiplier theorem for the Hodge-Kodaira operator. Zbl 1080.58024
Shigekawa, Ichiro
2005
The domain of a generator and the intertwining property. Zbl 0972.60080
Shigekawa, Ichiro
2000
A comparison theorem for eigenvalues of the covariant Laplacian. Zbl 0716.58030
Manabe, Shojiro; Shigekawa, Ichiro
1990
Exponential convergence of Markovian semigroups and their spectra on $$L^p$$-spaces. Zbl 1306.60107
Kusuoka, Seiichiro; Shigekawa, Ichiro
2014
Dual ultracontractivity and its applications. Zbl 1322.47040
Shigekawa, Ichiro
2014
Non-symmetric diffusions on a Riemannian manifold. Zbl 1200.58024
Shigekawa, Ichiro
2010
Schrödinger operators on the Wiener space. Zbl 1328.60157
Shigekawa, Ichiro
2007
Defective intertwining property and generator domain. Zbl 1113.47028
Shigekawa, Ichiro
2006
On equivalence of $$L^{p}$$-norms related to Schrödinger type operators on Riemannian manifolds. Zbl 1094.53034
Miyokawa, Tomohiro; Shigekawa, Ichiro
2006
$$L^p$$ multiplier theorem for the Hodge-Kodaira operator. Zbl 1080.58024
Shigekawa, Ichiro
2005
Stochastic analysis. Translated from the Japanese by Ichiro Shigekawa. Zbl 1064.60003
Shigekawa, Ichiro
2004
Orlicz norm equivalence for the Ornstein-Uhlenbeck operator. Zbl 1063.60083
Shigekawa, Ichiro
2004
Vanishing theorem of the Hodge-Kodaira operator for differential forms on a convex domain of the Wiener space. Zbl 1077.58022
Shigekawa, Ichiro
2003
Littlewood-Paley inequality for a diffusion satisfying the logarithmic Sobolev inequality and for the Brownian motion on a Riemannian manifold with boundary. Zbl 1016.58022
Shigekawa, Ichiro
2002
Semigroup domination on a Riemannian manifold with boundary. Zbl 0992.60081
Shigekawa, Ichiro
2000
The domain of a generator and the intertwining property. Zbl 0972.60080
Shigekawa, Ichiro
2000
$$L^ p$$ contraction semigroups for vector valued functions. Zbl 0886.47024
Shigekawa, Ichiro
1997
The Meyer inequality for the Ornstein-Uhlenbeck operator in $$L^1$$ and probabilistic proof of Stein’s $$L^p$$ multiplier theorem. Zbl 1010.60051
Shigekawa, Ichiro
1997
A Kähler metric on a based loop group and a covariant differentiation. Zbl 0867.53029
Shigekawa, Ichiro; Taniguchi, Setsuo
1996
An example of regular $$(r,p)$$-capacity and essential self-adjointness of a diffusion operator in infinite dimensions. Zbl 0855.31005
Shigekawa, Ichiro
1995
Differential calculus on a submanifold of an abstract Wiener space. II: Weitzenböck formula. Zbl 0836.60064
Kazumi, Tetsuya; Shigekawa, Ichiro
1995
A quasihomeomorphism on the Wiener space. Zbl 0821.60059
Shigekawa, Ichiro
1995
Logarithmic Sobolev inequalities and exponential integrability. Zbl 0846.46020
Aida, Shigeki; Masuda, Takao; Shigekawa, Ichiro
1994
Logarithmic Sobolev inequalities and spectral gaps: Perturbation theory. Zbl 0846.46019
Aida, Shigeki; Shigekawa, Ichiro
1994
Sobolev spaces of Banach-valued functions associated with a Markov process. Zbl 0801.60044
Shigekawa, Ichiro
1994
Differential calculus on a submanifold of an abstract Wiener space. I: Covariant derivative. Zbl 0829.46031
Kazumi, T.; Shigekawa, I.
1994
Sobolev spaces over the Wiener space based on an Ornstein-Uhlenbeck operator. Zbl 0777.60047
Shigekawa, Ichiro
1992
Measures of finite $$(r,p)$$-energy and potentials on a separable metric space. Zbl 0769.60069
Kazumi, Tetsuya; Shigekawa, Ichiro
1992
Littlewood-Paley-Stein inequality for a symmetric diffusion. Zbl 0764.60060
Shigekawa, Ichiro; Yoshida, Nobuo
1992
Dirichlet forms on separable metric spaces. Zbl 0818.60068
Shigekawa, Ichiro; Taniguchi, Setsuo
1992
Spectral properties of Schrödinger operators with magnetic fields for a spin $${1 \over{} 2}$$ particle. Zbl 0742.47002
Shigekawa, Ichiro
1991
Itô-Wiener expansions of holomorphic functions on the complex Wiener space. Zbl 0727.60053
Shigekawa, Ichiro
1991
A comparison theorem for eigenvalues of the covariant Laplacian. Zbl 0716.58030
Manabe, Shojiro; Shigekawa, Ichiro
1990
A probabilistic proof of the Gauss-Bonnet-Chern theorem for manifolds with boundary. Zbl 0704.58056
Shigekawa, Ichiro; Ueki, Naomasa; Watanabe, Shinzo
1989
A stochastic approach to the Riemann-Roch theorem. Zbl 0709.58036
Shigekawa, Ichiro; Ueki, Naomasa
1988
Eigenvalue problems for the Schrödinger operator with the magnetic field on a compact Riemann manifold. Zbl 0629.58023
Shigekawa, Ichiro
1987
Existence of invariant measures of diffusions on an abstract Wiener space. Zbl 0636.60080
Shigekawa, Ichiro
1987
De Rham-Hodge-Kodaira’s decomposition on an abstract Wiener space. Zbl 0611.58006
Shigekawa, Ichiro
1986
The Malliavin calculus and long time asymptotics of certain Wiener integrals. Zbl 0573.60055
Ikeda, Nobuyuki; Shigekawa, Ichiro; Taniguchi, Setsuo
1985
Limit theorems for stochastic flows of diffeomorphisms of jump type. Zbl 0548.60035
Matsumoto, Hiroyuki; Shigekawa, I.
1985
Transformations of the Brownian motion on a Riemannian symmetric space. Zbl 0518.60087
Shigekawa, Ichiro
1984
On a quasi everywhere existence of the local time of the 1-dimensional Brownian motion. Zbl 0551.60076
Shigekawa, Ichiro
1984
Transformations of the Brownian motion on the Lie group. Zbl 0563.58035
Shigekawa, Ichiro
1984
On stochastic horizontal lifts. Zbl 0487.60056
Shigekawa, Ichiro
1982
Derivatives of Wiener functionals and absolute continuity of induced measures. Zbl 0476.28008
Shigekawa, Ichiro
1980
Absolute continuity of probability laws of Wiener functionals. Zbl 0422.60032
Shigekawa, Ichiro
1978
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#### Cited by 348 Authors

 12 Léandre, Rémi 12 Röckner, Michael 11 Wang, Feng-Yu 10 Bogachev, Vladimir Igorevich 9 Albeverio, Sergio A. 9 Cruzeiro, Ana-Bela 9 Nualart, David 9 Shigekawa, Ichiro 7 Aida, Shigeki 6 Driver, Bruce K. 6 Ghanmi, Allal 6 Gordina, Maria 6 Intissar, Ahmed 6 Li, Xue-Mei 6 Ren, Jiagang 5 Bobkov, Sergey Germanovich 5 Elworthy, K. David 5 Haslinger, Friedrich 5 Ismail, Mourad El-Houssieny 5 Li, Xiang-Dong 5 Malliavin, Paul 5 Nourdin, Ivan 5 Tudor, Ciprian A. 5 Zakai, Moshe 5 Zhang, Xicheng 4 Goldys, Beniamin 4 Ledoux, Michel 4 Ogurisu, Osamu 4 Sanz-Solé, Marta 4 Taniguchi, Setsuo 3 Arai, Asao 3 Cattiaux, Patrick 3 Colbois, Bruno 3 Da Prato, Giuseppe 3 Fang, Shizan 3 Fukushima, Masatoshi 3 Götze, Friedrich W. 3 Hino, Masanori 3 Inahama, Yuzuru 3 Kosov, Egor D. 3 Kusuoka, Seiichiro Kusuoka 3 Maas, Jan 3 Nikitin, E. V. 3 Peccati, Giovanni 3 Pontier, Monique 3 Privault, Nicolas 3 Russo, Francesco 3 Savo, Alessandro 3 Thalmaier, Anton 3 van Neerven, Jan M. A. M. 3 Wang, Fengyu 3 Wang, Jian 3 Zhang, Tusheng S. 2 Airault, Hélène 2 Bakry, Dominique 2 Baudoin, Fabrice 2 Bismut, Jean-Michel 2 Breton, Jean-Christophe 2 Brzeźniak, Zdzisław 2 Cass, Thomas Richard 2 Chojnowska-Michalik, Anna 2 Cianchi, Andrea 2 Daletskii, Alexei 2 Darling, Richard W. R. 2 de la Pradelle, Arnaud 2 Deck, Thomas 2 Feyel, Denis 2 Friz, Peter Karl 2 Funaki, Tadahisa 2 Grong, Erlend 2 Gross, Leonard 2 Guillin, Arnaud 2 Güneysu, Batu 2 He, Kai 2 Helffer, Bernard 2 Hinz, Michael 2 Hirsch, Francis 2 Houdré, Christian 2 Imkeller, Peter 2 Intissar, Abdelkader 2 Iwatsuka, Akira 2 Kawabi, Hiroshi 2 Kondrat’yev, Yuriĭ Grygorovych 2 Kusuoka, Shigeo 2 Liu, Yong 2 Liu, Yuan 2 Long, Hongwei 2 Lunardi, Alessandra 2 Luo, Dejun 2 Lytvynov, Eugene W. 2 Mao, Yonghua 2 Maslowski, Bohdan 2 Mayer-Wolf, Eduardo 2 Melcher, Tai 2 Olivera, Christian 2 Ouyang, Cheng 2 Pallara, Diego 2 Pick, Luboš 2 Qian, Zhongmin M. 2 Raikov, Georgi D. ...and 248 more Authors
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#### Cited in 101 Serials

 83 Journal of Functional Analysis 20 Potential Analysis 18 Probability Theory and Related Fields 15 The Annals of Probability 13 Journal of Mathematical Analysis and Applications 13 Stochastic Processes and their Applications 10 Infinite Dimensional Analysis, Quantum Probability and Related Topics 9 Journal of Mathematical Physics 7 Transactions of the American Mathematical Society 6 Journal of Geometry and Physics 6 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 6 Statistics & Probability Letters 5 Reviews in Mathematical Physics 5 Kyoto Journal of Mathematics 4 Stochastics 4 Mathematische Nachrichten 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Bulletin des Sciences Mathématiques 3 Letters in Mathematical Physics 3 Advances in Mathematics 3 Journal of the Mathematical Society of Japan 3 Mathematische Annalen 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Stochastic Analysis and Applications 3 Revista Matemática Iberoamericana 3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 3 Journal of Mathematical Sciences (New York) 3 Integral Transforms and Special Functions 3 Bernoulli 3 Acta Mathematica Sinica. English Series 2 Israel Journal of Mathematics 2 Journal of Statistical Physics 2 Mathematical Notes 2 Annales de l’Institut Fourier 2 Duke Mathematical Journal 2 Mathematische Zeitschrift 2 Proceedings of the Japan Academy. Series A 2 Results in Mathematics 2 Journal of Theoretical Probability 2 Communications in Partial Differential Equations 2 NoDEA. Nonlinear Differential Equations and Applications 2 Doklady Mathematics 1 Applicable Analysis 1 Communications on Pure and Applied Mathematics 1 Journal d’Analyse Mathématique 1 Lithuanian Mathematical Journal 1 Mathematical Methods in the Applied Sciences 1 Russian Mathematical Surveys 1 Theory of Probability and its Applications 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annales Polonici Mathematici 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Applied Mathematics and Optimization 1 Archiv der Mathematik 1 Publications Mathématiques 1 International Journal of Mathematics and Mathematical Sciences 1 Integral Equations and Operator Theory 1 Journal of Approximation Theory 1 Journal of the London Mathematical Society. Second Series 1 Journal of Multivariate Analysis 1 Kodai Mathematical Journal 1 Memoirs of the American Mathematical Society 1 Osaka Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Annals of Global Analysis and Geometry 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Probabilités et Applications 1 Science in China. Series A 1 Japan Journal of Industrial and Applied Mathematics 1 Differential Geometry and its Applications 1 Expositiones Mathematicae 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Stochastics and Stochastics Reports 1 Indagationes Mathematicae. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Calculus of Variations and Partial Differential Equations 1 Applied and Computational Harmonic Analysis 1 Kyushu Journal of Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Positivity 1 Annals of Mathematics. Second Series 1 Communications in Contemporary Mathematics 1 Annales Henri Poincaré 1 Brazilian Journal of Probability and Statistics 1 Journal of Nonlinear Mathematical Physics 1 Journal of Evolution Equations 1 Discrete and Continuous Dynamical Systems. Series B 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Stochastics and Dynamics 1 Communications on Pure and Applied Analysis 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Mediterranean Journal of Mathematics 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Journal of the Korean Statistical Society 1 Complex Analysis and Operator Theory 1 Electronic Journal of Statistics 1 Discrete and Continuous Dynamical Systems. Series S ...and 1 more Serials
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#### Cited in 37 Fields

 235 Probability theory and stochastic processes (60-XX) 98 Global analysis, analysis on manifolds (58-XX) 70 Operator theory (47-XX) 68 Partial differential equations (35-XX) 50 Functional analysis (46-XX) 42 Quantum theory (81-XX) 30 Potential theory (31-XX) 24 Differential geometry (53-XX) 22 Measure and integration (28-XX) 15 Real functions (26-XX) 13 Topological groups, Lie groups (22-XX) 13 Special functions (33-XX) 11 Several complex variables and analytic spaces (32-XX) 11 Dynamical systems and ergodic theory (37-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 7 Statistical mechanics, structure of matter (82-XX) 4 Number theory (11-XX) 4 Ordinary differential equations (34-XX) 4 Difference and functional equations (39-XX) 4 Abstract harmonic analysis (43-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 Functions of a complex variable (30-XX) 3 Algebraic topology (55-XX) 3 Statistics (62-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 Combinatorics (05-XX) 2 Nonassociative rings and algebras (17-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Numerical analysis (65-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Integral equations (45-XX) 1 Manifolds and cell complexes (57-XX) 1 Information and communication theory, circuits (94-XX)

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