## Michor, Peter Wolfram

Compute Distance To:
 Author ID: michor.peter-w Published as: Michor, Peter W.; Michor, P. W.; Michor, P.; Michor, Peter; Michor, W Peter. more...less Homepage: http://www.mat.univie.ac.at/~michor/ External Links: MGP · ORCID · Wikidata · ResearchGate · MathOverflow · Math-Net.Ru · dblp · GND · IdRef · theses.fr
 Documents Indexed: 154 Publications since 1974, including 9 Books 3 Contributions as Editor · 1 Further Contribution Reviewing Activity: 79 Reviews Co-Authors: 67 Co-Authors with 118 Joint Publications 1,582 Co-Co-Authors
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### Co-Authors

 39 single-authored 28 Kriegl, Andreas 19 Bauer, Martin 15 Bruveris, Martins 15 Losik, Mark V. 14 Rainer, Armin 12 Alekseevskiĭ, Dmitriĭ Vladimirovich 10 Harms, Philipp 9 Mumford, David Bryant 5 Dubois-Violette, Michel 5 Marmo, Giuseppe 4 Grabowski, Janusz 3 Gil-Medrano, Olga 3 Kolář, Ivan 3 Sigmund, Karl 3 Slovák, Jan 2 Abbati, Maria Cristina 2 Čap, Andreas 2 Cirelli, Renzo 2 Kainz, Gerd 2 Kamber, Franz W. 2 Maeda, Yoshiaki 2 Manià, Alessandro 2 Micheli, Mario 2 Neretin, Yuriĭ Aleksandrovich 2 Popov, Vladimir Leonidovich 2 Ruppert, Wolfgang A. F. 2 Schichl, Hermann 2 Schicketanz, Hubert 2 Sigmund, Anna Maria 2 Vanžura, Jiří 1 Agricola, Ilka 1 Andai, Attila 1 Canarutto, Daniel 1 Cervera, Vicente 1 Chruściel, Piotr Tadeusz 1 Cigler, Johann 1 Cooper, James Bell 1 Delay, Erwann 1 Eastwood, Michael G. 1 Gindikin, Simon Grigorevich 1 Götze, Friedrich 1 Grötschel, Martin 1 Hoffmann-Ostenhof, Thomas 1 Hulek, Klaus 1 Ismagilov, Rais Sal’manovich 1 Khesin, Boris A. 1 Klassen, Eric Paul 1 Klinger, Paul 1 Kodama, Hiroki 1 Kostant, Bertram 1 Kriegl, P. 1 Lecomte, P. A. B. 1 Losert, Viktor 1 Marsland, Stephen R. 1 Mascaro, Francisca 1 Mauhart, Markus 1 Nadirashvili, Nikolai S. 1 Nebe, Gabriele 1 Neuwirther, Martin 1 Ochiai, Takushiro 1 Parusiński, Adam 1 Petz, Dénes 1 Prömel, Hans Jürgen 1 Ratiu, Tudor Stefan 1 Schachermayer, Walter 1 Shah, Jayant 1 Teichmann, Josef 1 Vaisman, Izu 1 Vinogradov, Aleksandr Mikhaĭlovich 1 Vizman, Cornelia 1 Vygen, Jens 1 Wegenkittl, K. 1 Woeginger, Gerhard Johannes 1 Yoshioka, Akira 1 Younes, Laurent
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### Serials

 8 Annals of Global Analysis and Geometry 8 Journal of Lie Theory 7 Differential Geometry and its Applications 6 Cahiers de Topologie et Géométrie Différentielle Catégoriques 4 Journal of Geometry and Physics 4 Archivum Mathematicum 4 Proceedings of the American Mathematical Society 4 Acta Mathematica Universitatis Comenianae. New Series 4 Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse. Sitzungsberichte. Abteilung II 4 Journal of Geometric Mechanics 3 Israel Journal of Mathematics 3 Journal of Pure and Applied Algebra 3 Internationale Mathematische Nachrichten 3 Revista Matemática Complutense 2 Journal of Mathematical Physics 2 Letters in Mathematical Physics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Journal of Functional Analysis 2 Mathematische Annalen 2 Monatshefte für Mathematik 2 Publicationes Mathematicae Debrecen 2 The Quarterly Journal of Mathematics. Oxford Second Series 2 Rendiconti del Seminario Matematico 2 Indagationes Mathematicae. New Series 2 Electronic Research Announcements of the American Mathematical Society 2 SIAM Journal on Imaging Sciences 1 Modern Physics Letters A 1 Communications in Mathematical Physics 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 The Mathematical Intelligencer 1 Acta Mathematica 1 Annales de l’Institut Fourier 1 Bulletin of the London Mathematical Society 1 Commentationes Mathematicae Universitatis Carolinae 1 Czechoslovak Mathematical Journal 1 Integral Equations and Operator Theory 1 Journal of Algebra 1 Journal of Combinatorics, Information & System Sciences 1 Journal of Differential Geometry 1 Mathematische Nachrichten 1 Sitzungsberichte. Abteilung II. Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse 1 Rendiconti. Scienze Matemàtiche e Applicazioni. A 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Geometric and Functional Analysis. GAFA 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Journal of Mathematical Imaging and Vision 1 Journal of Nonlinear Science 1 Calculus of Variations and Partial Differential Equations 1 Applied and Computational Harmonic Analysis 1 Izvestiya: Mathematics 1 Discrete and Continuous Dynamical Systems 1 The Journal of Fourier Analysis and Applications 1 Documenta Mathematica 1 Transformation Groups 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Journal of the European Mathematical Society (JEMS) 1 Moscow Mathematical Journal 1 International Journal of Geometric Methods in Modern Physics 1 Conference Proceedings and Lecture Notes in Mathematical Physics 1 Graduate Studies in Mathematics 1 Lecture Notes in Mathematics 1 Lecture Notes in Pure and Applied Mathematics 1 Mathematical Surveys and Monographs 1 Monografii Matematice (Timișoara) 1 Progress in Mathematics 1 Forum of Mathematics, Sigma 1 Abhandlungen der Akademie der Wissenschaften der DDR 1 Geometry, Imaging and Computing
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### Fields

 82 Global analysis, analysis on manifolds (58-XX) 44 Differential geometry (53-XX) 31 Functional analysis (46-XX) 23 Topological groups, Lie groups (22-XX) 16 Nonassociative rings and algebras (17-XX) 15 Partial differential equations (35-XX) 13 Dynamical systems and ergodic theory (37-XX) 10 Group theory and generalizations (20-XX) 10 Operator theory (47-XX) 9 Manifolds and cell complexes (57-XX) 8 Real functions (26-XX) 7 Category theory; homological algebra (18-XX) 6 Quantum theory (81-XX) 5 History and biography (01-XX) 5 Algebraic geometry (14-XX) 5 Associative rings and algebras (16-XX) 5 General topology (54-XX) 3 General and overarching topics; collections (00-XX) 3 Numerical analysis (65-XX) 3 Mechanics of particles and systems (70-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Algebraic topology (55-XX) 2 Relativity and gravitational theory (83-XX) 1 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-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 Statistics (62-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

134 Publications have been cited 2,449 times in 1,492 Documents Cited by Year
The convenient setting of global analysis. Zbl 0889.58001
Kriegl, Andreas; Michor, Peter W.
1997
Natural operations in differential geometry. Zbl 0782.53013
Kolář, Ivan; Michor, Peter W.; Slovák, Jan
1993
Manifolds of differentiable mappings. Zbl 0433.58001
Michor, P. W.
1980
Riemannian geometries on spaces of plane curves. Zbl 1101.58005
Michor, Peter W.; Mumford, David
2006
Topics in differential geometry. Zbl 1175.53002
Michor, Peter W.
2008
An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach. Zbl 1116.58007
Michor, Peter W.; Mumford, David
2007
A metric on shape space with explicit geodesics. Zbl 1142.58013
Younes, Laurent; Michor, Peter W.; Shah, Jayant; Mumford, David
2008
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Zbl 1083.58010
Michor, Peter W.; Mumford, David
2005
Overview of the geometries of shape spaces and diffeomorphism groups. Zbl 1310.58005
Bauer, Martin; Bruveris, Martins; Michor, Peter W.
2014
Connections on central bimodules in noncommutative differential geometry. Zbl 0867.53023
Dubois-Violette, Michel; Michor, Peter W.
1996
Sobolev metrics on shape space of surfaces. Zbl 1262.58004
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2011
The Riemannian manifold of all Riemannian metrics. Zbl 0739.58010
Gil-Medrano, Olga; Michor, Peter W.
1991
Choosing roots of polynomials smoothly. Zbl 0912.26006
Alekseevsky, Dmitri; Kriegl, Andreas; Michor, Peter W.; Losik, Mark
1998
Banach modules and functors on categories of Banach spaces. Zbl 0411.46044
Cigler, Johann; Losert, Viktor; Michor, Peter
1979
The convenient setting for real analytic mappings. Zbl 0738.46024
Kriegl, A.; Michor, P. W.
1990
Constructing reparameterization invariant metrics on spaces of plane curves. Zbl 1291.58002
Bauer, Martin; Bruveris, Martins; Marsland, Stephen; Michor, Peter W.
2014
Regular infinite dimensional Lie groups. Zbl 0893.22012
Kriegl, Andreas; Michor, Peter W.
1997
Geodesic completeness for Sobolev metrics on the space of immersed plane curves. Zbl 1315.58009
Bruveris, Martins; Michor, Peter W.; Mumford, David
2014
The convenient setting for non-quasianalytic Denjoy-Carleman differentiable mappings. Zbl 1178.46039
Kriegl, Andreas; Michor, Peter W.; Rainer, Armin
2009
Some geometric evolution equations arising as geodesic equations on groups of diffeomorphisms including the Hamiltonian approach. Zbl 1221.58006
Michor, Peter W.
2006
Extensions of super Lie algebras. Zbl 1098.17014
Alekseevsky, Dmitri; Michor, Peter W.; Ruppert, W. A. F.
2005
Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. Zbl 1288.35415
Bauer, Martin; Bruveris, Martins; Harms, Philipp; Michor, Peter W.
2013
Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation. Zbl 1246.58005
Bauer, Martin; Bruveris, Martins; Harms, Philipp; Michor, Peter W.
2012
The action of the diffeomorphism group on the space of immersions. Zbl 0783.58012
Cervera, Vicente; Mascaró, Francisca; Michor, Peter W.
1991
Natural transformations in differential geometry. Zbl 0654.58001
Kainz, Gerd; Michor, Peter W.
1987
On Euler’s equation and ‘EPDiff’. Zbl 1274.35277
Mumford, David; Michor, Peter W.
2013
The convenient setting for quasianalytic Denjoy-Carleman differentiable mappings. Zbl 1250.46018
Kriegl, Andreas; Michor, Peter W.; Rainer, Armin
2011
A zoo of diffeomorphism groups on $$\mathbb R^n$$. Zbl 1364.22009
Michor, Peter W.; Mumford, David
2013
Sobolev metrics on shape space. II: Weighted Sobolev metrics and almost local metrics. Zbl 1281.58003
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2012
The Riemann geometry of orbit spaces – the metric, geodesics and integrable systems. Zbl 1026.57028
Alekseevsky, Dmitri; Kriegl, Andreas; Losik, Mark; Michor, Peter W.
2003
Uniqueness of the Fisher-Rao metric on the space of smooth densities. Zbl 1347.58001
Bauer, Martin; Bruveris, Martins; Michor, Peter W.
2016
Derivations and non-commutative differential calculus. II. (Dérivations et calcul différentiel non commutatif. II.) Zbl 0829.16028
Dubois-Violette, Michel; Michor, Peter W.
1994
The Lie group of automorphisms of a principal bundle. Zbl 0692.58010
Abbati, M. C.; Cirelli, R.; Mania’, A.; Michor, P.
1989
Differentiable perturbation of unbounded operators. Zbl 1054.47014
Kriegl, Andreas; Michor, Peter W.
2003
The multigraded Nijenhuis-Richardson algebra, its universal property and applications. Zbl 0752.17019
Lecomte, P. A. B.; Michor, P. W.; Schicketanz, H.
1992
Almost local metrics on shape space of hypersurfaces in n-space. Zbl 1251.58002
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2012
Homology and modular classes of Lie algebroids. Zbl 1141.17018
Grabowski, Janusz; Marmo, Giuseppe; Michor, Peter W.
2006
$$n$$-ary Lie and associative algebras. Zbl 0928.17029
Michor, P. W.; Vinogradov, A. M.
1996
Sobolev metrics on the manifold of all Riemannian metrics. Zbl 1275.58007
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2013
Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds. Zbl 1280.58005
Micheli, M.; Michor, P. W.; Mumford, D.
2013
Why use Sobolev metrics on the space of curves. Zbl 1338.65043
Bauer, Martin; Bruveris, Martins; Michor, Peter W.
2016
Bounds on the multiplicity of eigenvalues for fixed membranes. Zbl 0949.35102
Hoffmann-Ostenhof, T.; Michor, P. W.; Nadirashvili, N.
1999
Knit products of graded Lie algebras and groups. Zbl 0954.17508
Michor, Peter W.
1990
Remarks on the Schouten-Nijenhuis bracket. Zbl 0646.53013
Michor, Peter W.
1987
Differential geometry of $$\mathfrak{g}$$-manifolds. Zbl 0854.53028
Alekseevsky, D. V.; Michor, Peter W.
1995
Homogeneous Sobolev metric of order one on diffeomorphism groups on real line. Zbl 1309.35064
Bauer, Martin; Bruveris, Martins; Michor, Peter W.
2014
An exotic zoo of diffeomorphism groups on $$\mathbb {R}^n$$. Zbl 1316.58008
Kriegl, Andreas; Michor, W Peter.; Rainer, Armin
2015
Sectional curvature in terms of the cometric, with applications to the Riemannian manifolds of landmarks. Zbl 1276.37047
Micheli, Mario; Michor, Peter W.; Mumford, David
2012
Smoothness of the action of the gauge transformation group on connections. Zbl 0618.58040
Abbati, M. C.; Cirelli, R.; Manià, A.; Michor, P.
1986
The convenient setting for Denjoy-Carleman differentiable mappings of Beurling and Roumieu type. Zbl 1331.26050
Kriegl, Andreas; Michor, Peter W.; Rainer, Armin
2015
Denjoy-Carleman differentiable perturbation of polynomials and unbounded operators. Zbl 1244.26028
Kriegl, Andreas; Michor, Peter W.; Rainer, Armin
2011
A generalization of Hamiltonian mechanics. Zbl 0587.58004
Michor, Peter W.
1985
Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II. Zbl 1290.35192
Bauer, Martin; Bruveris, Martins; Michor, Peter W.
2013
Choosing roots of polynomials smoothly. II. Zbl 1071.26009
Kriegl, Andreas; Losik, Mark; Michor, Peter W.
2004
On the geometry of the Virasoro-Bott group. Zbl 0945.58005
Michor, P. W.; Ratiu, T. S.
1998
Manifolds of smooth maps, II: The Lie group of diffeomorphisms of a non- compact smooth manifold. Zbl 0434.58011
Michor, P.
1980
Manifolds of smooth maps. IV: Theorem of de Rham. Zbl 0508.58012
Michor, P.
1983
A convenient setting for differential geometry and global analysis. Zbl 0548.58001
Michor, Peter
1984
Gauge theory for fiber bundles. Zbl 0953.53001
Michor, Peter W.
1991
Smooth $$\star$$-algebras. Zbl 1026.46062
Dubois-Violette, Michel; Kriegl, Andreas; Maeda, Yoshiaki; Michor, Peter W.
2001
Manifolds of smooth maps III: The principal bundle of embeddings of a non-compact smooth manifold. Zbl 0442.58011
Michor, P.
1980
$$R$$-transforms for Sobolev $$H^2$$-metrics on spaces of plane curves. Zbl 1315.35149
Bauer, Martin; Bruveris, Martins; Michor, Peter W.
2014
Poisson structures on the cotangent bundle of a Lie group or a principal bundle and their reductions. Zbl 0822.58016
Alekseevsky, D.; Grabowski, J.; Marmo, G.; Michor, P. W.
1994
A common generalization of the Frölicher-Nijenhuis bracket and the Schouten bracket for symmetric multivector fields. Zbl 0844.58002
Dubois-Violette, Michel; Michor, Peter W.
1995
Reflection groups on Riemannian manifolds. Zbl 1232.51010
Alekseevsky, Dmitri V.; Kriegl, Andreas; Losik, Mark; Michor, Peter W.
2007
Aspects of the theory of infinite dimensional manifolds. Zbl 0782.58011
Kriegl, Andreas; Michor, Peter W.
1991
Characters on algebras of smooth functions. Zbl 0691.58020
Kriegl, A.; Michor, P.; Schachermayer, W.
1989
Poisson structures on double Lie groups. Zbl 1020.17016
Alekseevsky, D.; Grabowski, J.; Marmo, G.; Michor, P. W.
1998
Differential geometry of Cartan connections. Zbl 0857.53011
Alekseevsky, D. V.; Michor, P. W.
1995
Product preserving functors of infinite dimensional manifolds. Zbl 0881.58010
Kriegl, A.; Michor, P. W.
1996
Manifolds of smooth maps. Zbl 0382.58009
Michor, P.
1978
Basic differential forms for actions of Lie groups. Zbl 0858.57038
Michor, Peter W.
1996
Lifting smooth curves over invariants for representations of compact Lie groups. Zbl 0960.22010
Alekseevsky, D. V.; Kriegl, A.; Losik, M.; Michor, P. W.
2000
Remarks on the Frölicher-Nijenhuis bracket. Zbl 0633.53024
Michor, Peter W.
1987
Functors and categories of Banach spaces. Tensor products, operator ideals and functors on categories of Banach spaces. Zbl 0369.46069
Michor, Peter W.
1978
More on the Frölicher-Nijenhuis bracket in noncommutative differential geometry. Zbl 0889.58011
Dubois-Violette, Michel; Michor, Peter W.
1997
A 2-cocycle on a symplectomorphism group. Zbl 1132.53043
Ismagilov, Rais S.; Losik, Mark; Michor, Peter W.
2006
Many parameter Hölder perturbation of unbounded operators. Zbl 1243.47031
Kriegl, Andreas; Michor, Peter W.; Rainer, Armin
2012
On polarizations in invariant theory. Zbl 1099.13012
Losik, Mark; Michor, Peter W.; Popov, Vladimir L.
2006
A convenient setting for differential geometry and global analysis. II. Zbl 0594.58011
Michor, Peter
1984
Lifting smooth curves over invariants for representations of compact Lie groups. II. Zbl 1062.22029
Kriegl, Andreas; Losik, Mark; Michor, Peter W.; Rainer, Armin
2005
Description of infinite-dimensional abelian regular Lie groups. Zbl 1012.22036
Michor, Peter; Teichmann, Josef
1999
Contributions to finite operator calculus in several variables. Zbl 0403.05004
Michor, P.
1979
The Frölicher-Nijenhuis bracket in non-commutative differential geometry. Zbl 0830.58002
Cap, A.; Kriegl, P.; Michor, P. W.; Vanžura, J.
1993
Curvature weighted metrics on shape space of hypersurfaces in $$n$$-space. Zbl 1237.58009
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2012
The exponential law for spaces of test functions and diffeomorphism groups. Zbl 1346.46019
Kriegl, Andreas; Michor, Peter W.; Rainer, Armin
2016
Some remarks on the Plücker relations. Zbl 1071.15501
Eastwood, Michael G.; Michor, Peter W.
2000
Completely integrable systems—a generalization. Zbl 1020.37538
Alekseevsky, D. V.; Grabowski, J.; Marmo, G.; Michor, P. W.
1997
Basic differential forms for actions of Lie groups. II. Zbl 0866.57027
Michor, Peter W.
1997
On the curvature of a certain Riemannian space of matrices. Zbl 1031.53109
Michor, Peter W.; Petz, Dénes; Andai, Attila
2000
Closed surfaces with different shapes that are indistinguishable by the SRNF. Zbl 1474.53029
Klassen, Eric; Michor, Peter W.
2020
Lifting smooth curves over invariants for representations of compact Lie groups. III. Zbl 1112.22003
Kriegl, Andreas; Losik, Mark; Michor, Peter W.; Rainer, Armin
2006
Pseudo-Riemannian metrics on spaces of bilinear structures. Zbl 0799.58013
Gil-Medrano, Olga; Michor, Peter W.; Neuwirther, Martin
1992
Commutators of flows and fields. Zbl 0784.58051
Mauhart, Markus; Michor, Peter W.
1992
$$n$$-transitivity of certain diffeomorphism groups. Zbl 0824.58014
Michor, P. W.; Vizman, C.
1994
The flow completion of the Burgers equation. Zbl 1062.37100
Khesin, Boris A.; Michor, Peter W.
2004
The generalized Cayley map from an algebraic group to its Lie algebra. Zbl 1072.20051
Kostant, Bertram; Michor, Peter W.
2003
Lifting mappings over invariants of finite groups. Zbl 1164.14009
Kriegl, A.; Losik, M.; Michor, P. W.; Rainer, A.
2008
Manifolds of differentiable maps. Zbl 0461.58005
Michor, Peter
1979
The division theorem on Banach spaces. Zbl 0467.58010
Michor, P.
1980
Closed surfaces with different shapes that are indistinguishable by the SRNF. Zbl 1474.53029
Klassen, Eric; Michor, Peter W.
2020
Fractional Sobolev metrics on spaces of immersions. Zbl 1441.58010
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2020
Geometry of the Fisher-Rao metric on the space of smooth densities on a compact manifold. Zbl 1415.58005
Bruveris, Martins; Michor, Peter W.
2019
Soliton solutions for the elastic metric on spaces of curves. Zbl 1396.58014
Bauer, Martin; Bruveris, Martins; Harms, Philipp; Michor, Peter W.
2018
Moser’s theorem on manifolds with corners. Zbl 1398.58004
Bruveris, Martins; Michor, Peter W.; Parusiński, Adam; Rainer, Armin
2018
Uniqueness of the Fisher-Rao metric on the space of smooth densities. Zbl 1347.58001
Bauer, Martin; Bruveris, Martins; Michor, Peter W.
2016
Why use Sobolev metrics on the space of curves. Zbl 1338.65043
Bauer, Martin; Bruveris, Martins; Michor, Peter W.
2016
The exponential law for spaces of test functions and diffeomorphism groups. Zbl 1346.46019
Kriegl, Andreas; Michor, Peter W.; Rainer, Armin
2016
Riemannian geometry of the space of volume preserving immersions. Zbl 1357.58013
Bauer, Martin; Michor, Peter W.; Müller, Olaf
2016
An exotic zoo of diffeomorphism groups on $$\mathbb {R}^n$$. Zbl 1316.58008
Kriegl, Andreas; Michor, W Peter.; Rainer, Armin
2015
The convenient setting for Denjoy-Carleman differentiable mappings of Beurling and Roumieu type. Zbl 1331.26050
Kriegl, Andreas; Michor, Peter W.; Rainer, Armin
2015
Overview of the geometries of shape spaces and diffeomorphism groups. Zbl 1310.58005
Bauer, Martin; Bruveris, Martins; Michor, Peter W.
2014
Constructing reparameterization invariant metrics on spaces of plane curves. Zbl 1291.58002
Bauer, Martin; Bruveris, Martins; Marsland, Stephen; Michor, Peter W.
2014
Geodesic completeness for Sobolev metrics on the space of immersed plane curves. Zbl 1315.58009
Bruveris, Martins; Michor, Peter W.; Mumford, David
2014
Homogeneous Sobolev metric of order one on diffeomorphism groups on real line. Zbl 1309.35064
Bauer, Martin; Bruveris, Martins; Michor, Peter W.
2014
$$R$$-transforms for Sobolev $$H^2$$-metrics on spaces of plane curves. Zbl 1315.35149
Bauer, Martin; Bruveris, Martins; Michor, Peter W.
2014
The Lagrangian Radon transform and the Weil representation. Zbl 1310.44005
Marmo, Giuseppe; Michor, Peter W.; Neretin, Yury A.
2014
Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. Zbl 1288.35415
Bauer, Martin; Bruveris, Martins; Harms, Philipp; Michor, Peter W.
2013
On Euler’s equation and ‘EPDiff’. Zbl 1274.35277
Mumford, David; Michor, Peter W.
2013
A zoo of diffeomorphism groups on $$\mathbb R^n$$. Zbl 1364.22009
Michor, Peter W.; Mumford, David
2013
Sobolev metrics on the manifold of all Riemannian metrics. Zbl 1275.58007
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2013
Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds. Zbl 1280.58005
Micheli, M.; Michor, P. W.; Mumford, D.
2013
Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II. Zbl 1290.35192
Bauer, Martin; Bruveris, Martins; Michor, Peter W.
2013
Rolling of Coxeter polyhedra along mirrors. Zbl 1318.52011
Alekseevski, Dmitri V.; Michor, Peter W.; Neretin, Yurii A.
2013
Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation. Zbl 1246.58005
Bauer, Martin; Bruveris, Martins; Harms, Philipp; Michor, Peter W.
2012
Sobolev metrics on shape space. II: Weighted Sobolev metrics and almost local metrics. Zbl 1281.58003
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2012
Almost local metrics on shape space of hypersurfaces in n-space. Zbl 1251.58002
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2012
Sectional curvature in terms of the cometric, with applications to the Riemannian manifolds of landmarks. Zbl 1276.37047
Micheli, Mario; Michor, Peter W.; Mumford, David
2012
Many parameter Hölder perturbation of unbounded operators. Zbl 1243.47031
Kriegl, Andreas; Michor, Peter W.; Rainer, Armin
2012
Curvature weighted metrics on shape space of hypersurfaces in $$n$$-space. Zbl 1237.58009
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2012
A generalization of Puiseux’s theorem and lifting curves over invariants. Zbl 1279.14058
Losik, Mark; Michor, Peter W.; Rainer, Armin
2012
Sobolev metrics on shape space of surfaces. Zbl 1262.58004
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2011
The convenient setting for quasianalytic Denjoy-Carleman differentiable mappings. Zbl 1250.46018
Kriegl, Andreas; Michor, Peter W.; Rainer, Armin
2011
Denjoy-Carleman differentiable perturbation of polynomials and unbounded operators. Zbl 1244.26028
Kriegl, Andreas; Michor, Peter W.; Rainer, Armin
2011
The convenient setting for non-quasianalytic Denjoy-Carleman differentiable mappings. Zbl 1178.46039
Kriegl, Andreas; Michor, Peter W.; Rainer, Armin
2009
Topics in differential geometry. Zbl 1175.53002
Michor, Peter W.
2008
A metric on shape space with explicit geodesics. Zbl 1142.58013
Younes, Laurent; Michor, Peter W.; Shah, Jayant; Mumford, David
2008
Lifting mappings over invariants of finite groups. Zbl 1164.14009
Kriegl, A.; Losik, M.; Michor, P. W.; Rainer, A.
2008
An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach. Zbl 1116.58007
Michor, Peter W.; Mumford, David
2007
Reflection groups on Riemannian manifolds. Zbl 1232.51010
Alekseevsky, Dmitri V.; Kriegl, Andreas; Losik, Mark; Michor, Peter W.
2007
Riemannian geometries on spaces of plane curves. Zbl 1101.58005
Michor, Peter W.; Mumford, David
2006
Some geometric evolution equations arising as geodesic equations on groups of diffeomorphisms including the Hamiltonian approach. Zbl 1221.58006
Michor, Peter W.
2006
Homology and modular classes of Lie algebroids. Zbl 1141.17018
Grabowski, Janusz; Marmo, Giuseppe; Michor, Peter W.
2006
A 2-cocycle on a symplectomorphism group. Zbl 1132.53043
Ismagilov, Rais S.; Losik, Mark; Michor, Peter W.
2006
On polarizations in invariant theory. Zbl 1099.13012
Losik, Mark; Michor, Peter W.; Popov, Vladimir L.
2006
Lifting smooth curves over invariants for representations of compact Lie groups. III. Zbl 1112.22003
Kriegl, Andreas; Losik, Mark; Michor, Peter W.; Rainer, Armin
2006
The homotopy type of the space of degree 0 – inmersed plane curves. Zbl 1104.58003
Kodama, Hiroki; Michor, Peter W.
2006
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Zbl 1083.58010
Michor, Peter W.; Mumford, David
2005
Extensions of super Lie algebras. Zbl 1098.17014
Alekseevsky, Dmitri; Michor, Peter W.; Ruppert, W. A. F.
2005
Lifting smooth curves over invariants for representations of compact Lie groups. II. Zbl 1062.22029
Kriegl, Andreas; Losik, Mark; Michor, Peter W.; Rainer, Armin
2005
Leray in Edelbach. Zbl 1189.01064
Sigmund, Anna Maria; Michor, Peter; Sigmund, Karl
2005
Choosing roots of polynomials smoothly. II. Zbl 1071.26009
Kriegl, Andreas; Losik, Mark; Michor, Peter W.
2004
The flow completion of the Burgers equation. Zbl 1062.37100
Khesin, Boris A.; Michor, Peter W.
2004
Completing Lie algebra actions to Lie group actions. Zbl 1066.22021
Kamber, Franz W.; Michor, Peter W.
2004
The Riemann geometry of orbit spaces – the metric, geodesics and integrable systems. Zbl 1026.57028
Alekseevsky, Dmitri; Kriegl, Andreas; Losik, Mark; Michor, Peter W.
2003
Differentiable perturbation of unbounded operators. Zbl 1054.47014
Kriegl, Andreas; Michor, Peter W.
2003
The generalized Cayley map from an algebraic group to its Lie algebra. Zbl 1072.20051
Kostant, Bertram; Michor, Peter W.
2003
Tensor fields and connections on holomorphic orbit spaces of finite groups. Zbl 1039.32029
Kriegl, Andreas; Losik, Mark; Michor, Peter W.
2003
Invariant tensor fields and orbit varieties for finite algebraic transformation groups. Zbl 1063.14055
Losik, Mark; Michor, Peter W.; Popov, Vladimir L.
2003
Smooth $$\star$$-algebras. Zbl 1026.46062
Dubois-Violette, Michel; Kriegl, Andreas; Maeda, Yoshiaki; Michor, Peter W.
2001
Lifting smooth curves over invariants for representations of compact Lie groups. Zbl 0960.22010
Alekseevsky, D. V.; Kriegl, A.; Losik, M.; Michor, P. W.
2000
Some remarks on the Plücker relations. Zbl 1071.15501
Eastwood, Michael G.; Michor, Peter W.
2000
On the curvature of a certain Riemannian space of matrices. Zbl 1031.53109
Michor, Peter W.; Petz, Dénes; Andai, Attila
2000
The flow completion of a manifold with vector field. Zbl 0955.37007
Kamber, Franz W.; Michor, Peter W.
2000
A note on $$n$$-ary Poisson brackets. Zbl 0986.53035
Michor, Peter W.; Vaisman, Izu
2000
Bounds on the multiplicity of eigenvalues for fixed membranes. Zbl 0949.35102
Hoffmann-Ostenhof, T.; Michor, P. W.; Nadirashvili, N.
1999
Description of infinite-dimensional abelian regular Lie groups. Zbl 1012.22036
Michor, Peter; Teichmann, Josef
1999
Choosing roots of polynomials smoothly. Zbl 0912.26006
Alekseevsky, Dmitri; Kriegl, Andreas; Michor, Peter W.; Losik, Mark
1998
On the geometry of the Virasoro-Bott group. Zbl 0945.58005
Michor, P. W.; Ratiu, T. S.
1998
Poisson structures on double Lie groups. Zbl 1020.17016
Alekseevsky, D.; Grabowski, J.; Marmo, G.; Michor, P. W.
1998
The convenient setting of global analysis. Zbl 0889.58001
Kriegl, Andreas; Michor, Peter W.
1997
Regular infinite dimensional Lie groups. Zbl 0893.22012
Kriegl, Andreas; Michor, Peter W.
1997
More on the Frölicher-Nijenhuis bracket in noncommutative differential geometry. Zbl 0889.58011
Dubois-Violette, Michel; Michor, Peter W.
1997
Completely integrable systems—a generalization. Zbl 1020.37538
Alekseevsky, D. V.; Grabowski, J.; Marmo, G.; Michor, P. W.
1997
Basic differential forms for actions of Lie groups. II. Zbl 0866.57027
Michor, Peter W.
1997
No slices on the space of generalized connections. Zbl 0924.58007
Michor, P. W.; Schichl, H.
1997
Connections on central bimodules in noncommutative differential geometry. Zbl 0867.53023
Dubois-Violette, Michel; Michor, Peter W.
1996
$$n$$-ary Lie and associative algebras. Zbl 0928.17029
Michor, P. W.; Vinogradov, A. M.
1996
Product preserving functors of infinite dimensional manifolds. Zbl 0881.58010
Kriegl, A.; Michor, P. W.
1996
Basic differential forms for actions of Lie groups. Zbl 0858.57038
Michor, Peter W.
1996
Characterizing algebras of $$C^ \infty$$-functions on manifolds. Zbl 0881.58001
Michor, P. W.; Vanžura, J.
1996
The Jacobi flow. Zbl 0919.53013
Michor, P. W.
1996
Differential geometry of $$\mathfrak{g}$$-manifolds. Zbl 0854.53028
Alekseevsky, D. V.; Michor, Peter W.
1995
A common generalization of the Frölicher-Nijenhuis bracket and the Schouten bracket for symmetric multivector fields. Zbl 0844.58002
Dubois-Violette, Michel; Michor, Peter W.
1995
Differential geometry of Cartan connections. Zbl 0857.53011
Alekseevsky, D. V.; Michor, P. W.
1995
Derivations and non-commutative differential calculus. II. (Dérivations et calcul différentiel non commutatif. II.) Zbl 0829.16028
Dubois-Violette, Michel; Michor, Peter W.
1994
Poisson structures on the cotangent bundle of a Lie group or a principal bundle and their reductions. Zbl 0822.58016
Alekseevsky, D.; Grabowski, J.; Marmo, G.; Michor, P. W.
1994
$$n$$-transitivity of certain diffeomorphism groups. Zbl 0824.58014
Michor, P. W.; Vizman, C.
1994
Geodesics on spaces of almost Hermitian structures. Zbl 0821.53031
Gil-Medrano, Olga; Michor, Peter W.
1994
75 years of Radon transform. Proceedings of the conference held at the Erwin Schrödinger International Institute for Mathematical Physics in Vienna, Austria, August 31-September 4, 1992. Zbl 0814.00012
1994
Natural operations in differential geometry. Zbl 0782.53013
Kolář, Ivan; Michor, Peter W.; Slovák, Jan
1993
The Frölicher-Nijenhuis bracket in non-commutative differential geometry. Zbl 0830.58002
Cap, A.; Kriegl, P.; Michor, P. W.; Vanžura, J.
1993
More smoothly real compact spaces. Zbl 0813.46026
Kriegl, Andreas; Michor, Peter W.
1993
Characteristic classes for $$G$$-structures. Zbl 0793.53028
Alekseevskij, D. V.; Michor, P. W.
1993
A quantum-group-like structure on noncommutative 2-tori. Zbl 0849.17012
Cap, Andreas; Michor, Peter W.; Schichl, Hermann
1993
The multigraded Nijenhuis-Richardson algebra, its universal property and applications. Zbl 0752.17019
Lecomte, P. A. B.; Michor, P. W.; Schicketanz, H.
1992
Pseudo-Riemannian metrics on spaces of bilinear structures. Zbl 0799.58013
Gil-Medrano, Olga; Michor, Peter W.; Neuwirther, Martin
1992
Commutators of flows and fields. Zbl 0784.58051
Mauhart, Markus; Michor, Peter W.
1992
All unitary representations admit moment mappings. Zbl 0795.22006
Michor, P. W.
1992
The Riemannian manifold of all Riemannian metrics. Zbl 0739.58010
Gil-Medrano, Olga; Michor, Peter W.
1991
...and 34 more Documents
all top 5

### Cited by 1,622 Authors

 62 Michor, Peter Wolfram 31 Bauer, Martin 28 Mikulski, Włodzimierz M. 28 Rainer, Armin 22 Bruveris, Martins 21 Kolář, Ivan 18 Majid, Shahn 17 Kriegl, Andreas 17 Srivastava, Anuj 16 Neeb, Karl-Hermann 15 Schmeding, Alexander 14 Glöckner, Helge 13 Kolev, Boris 13 Nigsch, Eduard Albert 12 Doupovec, Miroslav 11 Gay-Balmaz, François 11 Marmo, Giuseppe 11 Modin, Klas 10 Grabowski, Janusz 10 Harms, Philipp 10 Vialard, François-Xavier 10 Vizman, Cornelia 9 Abbassi, Mohamed Tahar Kadaoui 9 Helffer, Bernard 9 Holm, Darryl D. 9 Kurek, Jan 9 Palese, Marcella 9 Ratiu, Tudor Stefan 8 Beggs, Edwin J. 8 Beltiţă, Daniel 8 Francaviglia, Mauro 8 Masson, Thierry 8 Muñoz Masqué, Jaime 8 Preston, Stephen C. 8 Rejzner, Katarzyna 8 Trouvé, Alain 8 Welker, Kathrin 7 Agore, Ana-Loredana 7 Charon, Nicolas 7 Dubois-Violette, Michel 7 Escher, Joachim 7 Klassen, Eric Paul 7 Marsland, Stephen R. 7 Navarro Garmendia, José 7 Schulz, Volker H. 7 Segev, Reuven 7 Vitolo, Raffaele F. 7 Wockel, Christoph 6 Canarutto, Daniel 6 de León Rodríguez, Manuel 6 Domański, Pawel Jan 6 Epstein, Marcelo 6 Esen, Oğul 6 Fatibene, Lorenzo 6 Giordano, Paolo Robuffo 6 Khavkine, Igor 6 Kosmann-Schwarzbach, Yvette 6 Kurtek, Sebastian 6 Laurent-Gengoux, Camille 6 Losik, Mark V. 6 Magnot, Jean-Pierre 6 Mumford, David Bryant 6 Needham, Tom 6 Pelletier, Fernand 6 Rotkiewicz, Mikołaj 6 Rybicki, Tomasz 6 Schenkel, Alexander 6 Shurygin, Vadim V. jun. 6 Siebenborn, Martin 6 Teichmann, Josef 6 Vorobiev, Yurii 6 Younes, Laurent 5 Abbati, Maria Cristina 5 Alekseevskiĭ, Dmitriĭ Vladimirovich 5 Bérard, Pierre H. 5 Bloch, Anthony Michael 5 Čap, Andreas 5 Diez, Tobias 5 Fredenhagen, Klaus 5 Galanis, George N. 5 Helemskii, Alexander Ya. 5 Hochgerner, Simon 5 Jóźwikowski, Michał 5 Kureš, Miroslav 5 Laux, Tim 5 McLachlan, Robert I. 5 Mennucci, Andrea Carlo Giuseppe 5 Militaru, Gigel 5 Perrone, Domenico 5 Rumpf, Martin 5 Schindl, Gerhard 5 Sommer, Stefan 5 Sütlü, Serkan 5 Winterroth, Ekkehart 4 Benayadi, Saïd 4 Benini, Marco 4 Bhowmick, Jyotishman 4 Biström, Peter 4 Bonet Solves, José 4 Boulabiar, Karim Mohamed ...and 1,522 more Authors
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### Cited in 320 Serials

 80 Journal of Geometry and Physics 71 Differential Geometry and its Applications 58 Annals of Global Analysis and Geometry 37 Communications in Mathematical Physics 35 Journal of Mathematical Physics 33 International Journal of Geometric Methods in Modern Physics 28 Journal of Functional Analysis 28 Monatshefte für Mathematik 27 Journal of Geometric Mechanics 24 Letters in Mathematical Physics 23 Reports on Mathematical Physics 22 Czechoslovak Mathematical Journal 20 Advances in Mathematics 20 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 18 Journal of Mathematical Imaging and Vision 18 International Journal of Computer Vision 17 Transformation Groups 16 Calculus of Variations and Partial Differential Equations 15 SIAM Journal on Imaging Sciences 14 Journal of Pure and Applied Algebra 14 The Journal of Geometric Analysis 13 Annales de l’Institut Fourier 13 Cahiers de Topologie et Géométrie Différentielle Catégoriques 13 Proceedings of the American Mathematical Society 12 Journal of Mathematical Analysis and Applications 12 Mathematische Zeitschrift 12 Transactions of the American Mathematical Society 12 Indagationes Mathematicae. New Series 12 Journal of Mathematical Sciences (New York) 11 Annali di Matematica Pura ed Applicata. Serie Quarta 11 Journal of Differential Equations 10 Israel Journal of Mathematics 10 Acta Applicandae Mathematicae 10 Journal of High Energy Physics 9 Archive for Rational Mechanics and Analysis 9 Classical and Quantum Gravity 9 Communications in Algebra 9 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 9 Geometriae Dedicata 9 Mathematische Annalen 9 Topology and its Applications 8 Journal of Nonlinear Science 8 Foundations of Computational Mathematics 7 General Relativity and Gravitation 7 Nuclear Physics. B 7 Reviews in Mathematical Physics 7 Journal of Algebra 7 Quarterly of Applied Mathematics 7 Annals of Physics 7 Lobachevskii Journal of Mathematics 7 Communications in Mathematics 6 Rocky Mountain Journal of Mathematics 6 Demonstratio Mathematica 6 Physica D 6 Linear Algebra and its Applications 6 Expositiones Mathematicae 6 SIAM Journal on Optimization 6 Applied Categorical Structures 6 Discrete and Continuous Dynamical Systems 6 Annales Henri Poincaré 6 Bulletin of the Brazilian Mathematical Society. New Series 6 Information Geometry 5 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 5 Numerische Mathematik 5 Rendiconti del Seminario Matematico della Università di Padova 5 Advances in Applied Clifford Algebras 5 Geometry & Topology 5 Cahiers de Topologie et Géométrie Différentielle Catégoriques 5 Mediterranean Journal of Mathematics 5 Analysis and Mathematical Physics 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Nonlinearity 4 Theoretical and Mathematical Physics 4 Archivum Mathematicum 4 Duke Mathematical Journal 4 International Journal of Mathematics and Mathematical Sciences 4 Mathematische Nachrichten 4 Memoirs of the American Mathematical Society 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Forum Mathematicum 4 International Journal of Mathematics 4 MSCS. Mathematical Structures in Computer Science 4 Theory and Applications of Categories 4 Revista Matemática Complutense 4 Journal of the European Mathematical Society (JEMS) 4 Acta Mathematica Sinica. English Series 4 Journal of Nonlinear Mathematical Physics 4 Journal of Homotopy and Related Structures 3 Inverse Problems 3 Physics Letters. A 3 Studia Mathematica 3 Acta Mathematica 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Applied Mathematics and Computation 3 Compositio Mathematica 3 Integral Equations and Operator Theory 3 Manuscripta Mathematica 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Results in Mathematics 3 SIAM Journal on Control and Optimization ...and 220 more Serials
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### Cited in 60 Fields

 591 Global analysis, analysis on manifolds (58-XX) 550 Differential geometry (53-XX) 214 Functional analysis (46-XX) 147 Topological groups, Lie groups (22-XX) 145 Partial differential equations (35-XX) 141 Quantum theory (81-XX) 125 Dynamical systems and ergodic theory (37-XX) 114 Nonassociative rings and algebras (17-XX) 94 Manifolds and cell complexes (57-XX) 84 Numerical analysis (65-XX) 82 Relativity and gravitational theory (83-XX) 80 Mechanics of particles and systems (70-XX) 74 Calculus of variations and optimal control; optimization (49-XX) 61 Category theory; homological algebra (18-XX) 60 Several complex variables and analytic spaces (32-XX) 60 Computer science (68-XX) 58 Statistics (62-XX) 57 Algebraic topology (55-XX) 51 Associative rings and algebras (16-XX) 48 Real functions (26-XX) 46 Operator theory (47-XX) 41 Algebraic geometry (14-XX) 35 Probability theory and stochastic processes (60-XX) 31 Group theory and generalizations (20-XX) 31 Fluid mechanics (76-XX) 27 Ordinary differential equations (34-XX) 27 Mechanics of deformable solids (74-XX) 26 Information and communication theory, circuits (94-XX) 24 Geometry (51-XX) 23 Systems theory; control (93-XX) 22 Functions of a complex variable (30-XX) 22 General topology (54-XX) 21 Commutative algebra (13-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 16 Mathematical logic and foundations (03-XX) 16 Biology and other natural sciences (92-XX) 14 Abstract harmonic analysis (43-XX) 13 Combinatorics (05-XX) 13 Operations research, mathematical programming (90-XX) 11 General and overarching topics; collections (00-XX) 11 Statistical mechanics, structure of matter (82-XX) 9 Field theory and polynomials (12-XX) 7 History and biography (01-XX) 7 Measure and integration (28-XX) 7 Convex and discrete geometry (52-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 4 $$K$$-theory (19-XX) 4 Special functions (33-XX) 4 Integral transforms, operational calculus (44-XX) 4 Astronomy and astrophysics (85-XX) 3 Number theory (11-XX) 3 Geophysics (86-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Potential theory (31-XX) 2 Difference and functional equations (39-XX) 2 Approximations and expansions (41-XX) 2 Optics, electromagnetic theory (78-XX) 1 General algebraic systems (08-XX) 1 Integral equations (45-XX)

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