## Bruning, Erwin Albert Karl

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 Author ID: bruning.erwin-a-k Published as: Brüning, E.; Brüning, Erwin; Brüning, Erwin A. K.; Bruning, Erwin A. K.; Brüning, E. A. K.; Bruening, Erwin more...less Homepage: http://math.ukzn.ac.za/~erwin/
 Documents Indexed: 45 Publications since 1981, including 6 Books 1 Contribution as Editor Co-Authors: 11 Co-Authors with 28 Joint Publications 360 Co-Co-Authors
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### Co-Authors

 18 single-authored 12 Nagamachi, Shigeaki 7 Blanchard, Philippe 4 Petruccione, Francesco 3 Gesztesy, Fritz 2 Xu, Chongming 1 Chruściński, Dariusz 1 Coule, David H. 1 Demuth, Michael 1 Mäkelä, Helena P. 1 Messina, Antonino 1 Wu, Xuejun
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### Serials

 8 Journal of Mathematical Physics 3 Open Systems & Information Dynamics 2 Letters in Mathematical Physics 2 Physics Letters. A 2 Reports on Mathematical Physics 2 Reviews in Mathematical Physics 2 Progress in Mathematical Physics 1 Applicable Analysis 1 Classical and Quantum Gravity 1 General Relativity and Gravitation 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 1 Journal of Differential Equations 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Quaestiones Mathematicae 1 Complex Variables. Theory and Application 1 Journal of Physics A: Mathematical and General 1 Communications on Applied Nonlinear Analysis 1 Journal of Modern Optics 1 Journal of Mathematics. The University of Tokushima 1 Complex Variables and Elliptic Equations 1 Lecture Notes in Physics 1 Texts and Monographs in Physics
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### Fields

 22 Functional analysis (46-XX) 22 Quantum theory (81-XX) 14 Operator theory (47-XX) 9 Partial differential equations (35-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 2 Functions of a complex variable (30-XX) 2 Relativity and gravitational theory (83-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX)

### Citations contained in zbMATH Open

23 Publications have been cited 104 times in 88 Documents Cited by Year
Variational methods in mathematical physics. A unified approach. Transl. from the German by Gillian M. Hayes. Zbl 0756.49023
Blanchard, Philippe; Brüning, Erwin
1992
Relativistic quantum field theory with a fundamental length. Zbl 1071.81078
Brüning, E.; Nagamachi, S.
2004
Hyperfunction quantum field theory: Basic structural results. Zbl 0703.46050
Brüning, Erwin; Nagamachi, Shigeaki
1989
Mathematical methods in physics. Distributions, Hilbert space operators, variational methods, and applications in quantum physics. 2nd ed. Zbl 1330.46001
Blanchard, Philippe; Brüning, Erwin
2015
Parametrizations of density matrices. Zbl 1356.81244
Brüning, E.; Mäkelä, H.; Messina, A.; Petruccione, F.
2012
Continuity of wave and scattering operators with respect to interactions. Zbl 0523.47008
Bruening, Erwin; Gesztesy, F.
1983
Parametrizing density matrices for composite quantum systems. Zbl 1188.81040
Brüning, Erwin; Chruściński, Dariusz; Petruccione, Francesco
2008
Direkte Methoden der Variationsrechnung. Ein Lehrbuch. Zbl 0488.49001
Blanchard, Philippe; Brüning, Erwin
1982
Density matrices and their time evolution. Zbl 1145.81015
Brüning, E.; Petruccione, F.
2008
Edge of the wedge theorem for tempered ultra-hyperfunctions. Zbl 1303.46030
Brüning, E.; Nagamachi, S.
2014
Mathematical methods in physics. Distributions, Hilbert space operators, and variational methods. Zbl 1019.46001
Blanchard, Philippe; Brüning, Erwin
2002
Hyperfunction quantum field theory: Localized fields without localized test functions. Zbl 1029.81048
Nagamachi, S.; Brüning, E.
2003
Closure of field operators, asymptotic abelianness, and vacuum structure in hyperfunction quantum field theory. Zbl 0986.81069
Brüning, E.; Nagamachi, S.
1998
A new class of Wick powers of generalized free fields. Zbl 0556.46044
Brüning, Erwin
1984
When is a field a Jacobi-field ? A characterization of states on tensor algebras. Zbl 0612.47034
Brüning, Erwin
1986
The n-field-irreducible part of a $$n$$-point functional. Zbl 0476.46059
Brüning, Erwin
1981
On the variational approach to semilinear elliptic equations with scale- covariance. Zbl 0701.35065
Brüning, Erwin
1990
Invariance of the essential spectra for perturbations with unbounded hard cores. Zbl 0632.47009
Brüning, E.; Demuth, M.; Gesztesy, F.
1987
Hyperfunction quantum field theory: Analytic structure, modular aspects, and local observable algebras. Zbl 1013.81034
Nagamachi, S.; Brüning, E.
2001
Solution of a linearized model of Heisenberg’s fundamental equation. II. Zbl 1152.81354
Brüning, E.; Nagamachi, S.
2008
On the construction of fields and the topological role of Jacobi fields. Zbl 0591.46059
Brüning, Erwin
1985
A note on solutions of two-dimensional semilinear elliptic vector-field equations with strong nonlinearity. Zbl 0703.35056
Brüning, E.
1989
Remarks on the structure of states of composite quantum systems and envariance. Zbl 1242.81023
Blanchard, Ph.; Brüning, E.
2006
Mathematical methods in physics. Distributions, Hilbert space operators, variational methods, and applications in quantum physics. 2nd ed. Zbl 1330.46001
Blanchard, Philippe; Brüning, Erwin
2015
Edge of the wedge theorem for tempered ultra-hyperfunctions. Zbl 1303.46030
Brüning, E.; Nagamachi, S.
2014
Parametrizations of density matrices. Zbl 1356.81244
Brüning, E.; Mäkelä, H.; Messina, A.; Petruccione, F.
2012
Parametrizing density matrices for composite quantum systems. Zbl 1188.81040
Brüning, Erwin; Chruściński, Dariusz; Petruccione, Francesco
2008
Density matrices and their time evolution. Zbl 1145.81015
Brüning, E.; Petruccione, F.
2008
Solution of a linearized model of Heisenberg’s fundamental equation. II. Zbl 1152.81354
Brüning, E.; Nagamachi, S.
2008
Remarks on the structure of states of composite quantum systems and envariance. Zbl 1242.81023
Blanchard, Ph.; Brüning, E.
2006
Relativistic quantum field theory with a fundamental length. Zbl 1071.81078
Brüning, E.; Nagamachi, S.
2004
Hyperfunction quantum field theory: Localized fields without localized test functions. Zbl 1029.81048
Nagamachi, S.; Brüning, E.
2003
Mathematical methods in physics. Distributions, Hilbert space operators, and variational methods. Zbl 1019.46001
Blanchard, Philippe; Brüning, Erwin
2002
Hyperfunction quantum field theory: Analytic structure, modular aspects, and local observable algebras. Zbl 1013.81034
Nagamachi, S.; Brüning, E.
2001
Closure of field operators, asymptotic abelianness, and vacuum structure in hyperfunction quantum field theory. Zbl 0986.81069
Brüning, E.; Nagamachi, S.
1998
Variational methods in mathematical physics. A unified approach. Transl. from the German by Gillian M. Hayes. Zbl 0756.49023
Blanchard, Philippe; Brüning, Erwin
1992
On the variational approach to semilinear elliptic equations with scale- covariance. Zbl 0701.35065
Brüning, Erwin
1990
Hyperfunction quantum field theory: Basic structural results. Zbl 0703.46050
Brüning, Erwin; Nagamachi, Shigeaki
1989
A note on solutions of two-dimensional semilinear elliptic vector-field equations with strong nonlinearity. Zbl 0703.35056
Brüning, E.
1989
Invariance of the essential spectra for perturbations with unbounded hard cores. Zbl 0632.47009
Brüning, E.; Demuth, M.; Gesztesy, F.
1987
When is a field a Jacobi-field ? A characterization of states on tensor algebras. Zbl 0612.47034
Brüning, Erwin
1986
On the construction of fields and the topological role of Jacobi fields. Zbl 0591.46059
Brüning, Erwin
1985
A new class of Wick powers of generalized free fields. Zbl 0556.46044
Brüning, Erwin
1984
Continuity of wave and scattering operators with respect to interactions. Zbl 0523.47008
Bruening, Erwin; Gesztesy, F.
1983
Direkte Methoden der Variationsrechnung. Ein Lehrbuch. Zbl 0488.49001
Blanchard, Philippe; Brüning, Erwin
1982
The n-field-irreducible part of a $$n$$-point functional. Zbl 0476.46059
Brüning, Erwin
1981
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### Cited by 117 Authors

 12 Bruning, Erwin Albert Karl 8 Solov’ev, Mikhaĭl Aleksandrovich 7 Nagamachi, Shigeaki 6 Auchmuty, Giles 4 Franco, Daniel H. T. 4 Siudeja, Bartłomiej Andrzej 2 Albeverio, Sergio A. 2 Gesztesy, Fritz 2 Lykina, Valeriya 2 Petruccione, Francesco 2 Smirnov, Alexander G. 2 Suwa, Masanori 2 Wreszinski, Walter F. 2 Yoshino, Kunio 1 Accardi, Luigi 1 Alexander, James Crew 1 Alves, Magno Branco 1 Antontsev, Stanislav Nikolaevich 1 Aste, Andreas 1 Baake, Michael 1 Barhoumi, Abdessatar 1 Batra, Romesh C. 1 Beesley, Jonathan J. 1 Bonizzoni, Francesca 1 Borovyk, Vita 1 Bozejko, Marek 1 Bracken, Paul Francis 1 Chabrowski, Jan H. 1 Chruściński, Dariusz 1 Crowder, Tanner 1 de Gosson, Maurice Alexis 1 Debrouwere, Andreas 1 dell’Isola, Francesco 1 Demuth, Michael 1 El Zafarani, Rasha M. 1 Falcó, Antonio 1 Feng, Johnny 1 Frettlöh, Dirk 1 Friedland, Shmuel 1 Ge, Jingtong 1 Girouard, Alexandre 1 Grossi, Ricardo Oscar 1 Hiesmayr, Beatrix C. 1 Høegh-Krohn, Raphael J. 1 Hou, Jinchuan 1 Huber, Marcus J. 1 Ikoma, Norihisa 1 Il’in, Nikolaĭ Borisovich 1 Jia, Wenyao 1 Karpukhin, Mikhail A. 1 Karwowski, Witold 1 Kellendonk, Johannes 1 Klouček, Petr 1 Kononets, Yu. V. 1 Kulczycki, Tadeusz 1 Kwaśnicki, Mateusz 1 Lagacé, Jean 1 Landsman, Nicolaas P. 1 Laugesen, Richard Snyder 1 Le Bris, Claude 1 Lefton, Lew E. 1 Leschke, Hajo 1 Lions, Pierre-Louis 1 Liskevich, Vitaliĭ A. 1 Lopes, Orlando Francisco 1 Lychkovskiy, Oleg V. 1 Lytvynov, Eugene W. 1 Makarov, Konstantin A. 1 Mäkelä, Helena P. 1 Manavi, Amir 1 Man’ko, Vladimir Ivanovich 1 Markovich, Liubov A. 1 Martin, Keye 1 Matsutani, Shigeki 1 Maziero, Jonas 1 Messina, Antonino 1 Moretti, Valter 1 Moschella, Ugo 1 Nigam, Nilima 1 Nobile, Fabio 1 Nouy, Anthony 1 Perugia, Ilaria 1 Pickenhain, Sabine 1 Polito, Caio M. M. 1 Pradovera, Davide 1 Raffo, Javier Leandro 1 Renoldi, Luiz H. 1 Riahi, Anis 1 Richard, Serge 1 Rivas, Mauricio A. 1 Robinson, Stephen B. 1 Rothlauf, Sebastian 1 Ruder, Rainer 1 Schmidt, Andreas Ullrich 1 Sciarra, Giulio 1 Shehata, Enas M. 1 Shimosako, Yoshiyuki 1 Shmarev, Sergei I. 1 Shpagina, E. 1 Spengler, Christoph ...and 17 more Authors
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### Cited in 52 Serials

 14 Journal of Mathematical Physics 4 Letters in Mathematical Physics 3 Journal of Mathematical Analysis and Applications 3 Journal of Statistical Physics 3 Theoretical and Mathematical Physics 3 Numerical Functional Analysis and Optimization 3 Infinite Dimensional Analysis, Quantum Probability and Related Topics 2 Communications in Mathematical Physics 2 Reviews in Mathematical Physics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Foundations of Physics 2 Complex Variables and Elliptic Equations 2 Journal of Physics A: Mathematical and Theoretical 1 Acta Mechanica 1 Applicable Analysis 1 International Journal of Theoretical Physics 1 Journal of Engineering Mathematics 1 Mathematical Methods in the Applied Sciences 1 Mathematics of Computation 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 1 Applied Mathematics and Optimization 1 Duke Mathematical Journal 1 Journal of Differential Equations 1 Journal of Functional Analysis 1 Journal of Optimization Theory and Applications 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerische Mathematik 1 Proceedings of the American Mathematical Society 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Quarterly of Applied Mathematics 1 Rendiconti del Seminario Matematico della Università di Padova 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Annales Scientifiques de l’Université Blaise Pascal Clermont-Ferrand II. Probabilités et Applications 1 Geometric and Functional Analysis. GAFA 1 Communications in Partial Differential Equations 1 Journal of Elasticity 1 Bulletin of the American Mathematical Society. New Series 1 Applied and Computational Harmonic Analysis 1 Integral Transforms and Special Functions 1 Open Systems & Information Dynamics 1 Journal of High Energy Physics 1 International Journal of Modern Physics C 1 Journal of Modern Optics 1 Foundations of Computational Mathematics 1 Portugaliae Mathematica. Nova Série 1 Proceedings of the Steklov Institute of Mathematics 1 Asian-European Journal of Mathematics 1 Advances in Mathematical Physics 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Evolution Equations and Control Theory 1 Journal of Function Spaces 1 AIMS Mathematics
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### Cited in 30 Fields

 41 Quantum theory (81-XX) 31 Functional analysis (46-XX) 24 Partial differential equations (35-XX) 12 Operator theory (47-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Numerical analysis (65-XX) 4 Probability theory and stochastic processes (60-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Mechanics of deformable solids (74-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Integral transforms, operational calculus (44-XX) 2 Computer science (68-XX) 2 Fluid mechanics (76-XX) 2 Operations research, mathematical programming (90-XX) 1 Associative rings and algebras (16-XX) 1 $$K$$-theory (19-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX)