The early proofs of the theorem of Campbell, Baker, Hausdorff, and Dynkin
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Publication:420535
DOI10.1007/s00407-012-0095-8zbMath1245.01002OpenAlexW2000235175WikidataQ56212033 ScholiaQ56212033MaRDI QIDQ420535
Rüdiger Achilles, Andrea Bonfiglioli
Publication date: 22 May 2012
Published in: Archive for History of Exact Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00407-012-0095-8
History of mathematics in the 20th century (01A60) History of mathematics in the 19th century (01A55) Research exposition (monographs, survey articles) pertaining to history and biography (01-02) History of topological groups (22-03)
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Cites Work
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- Topics in noncommutative algebra. The theorem of Campbell, Baker, Hausdorff and Dynkin
- On Lie supergroups and superbundles defined via the Baker-Campbell-Hausdorff formula
- The Lie theory of connected pro-Lie groups. A structure theory for pro-Lie algebras, pro-Lie groups, and connected locally compact groups
- Convergence of the Magnus series
- Towards a Lie theory of locally convex groups
- Balls and metrics defined by vector fields. I: Basic properties
- On Sophus Lie's fundamental theorem
- Convergence proof for Goldberg's exponential series
- A note on the Campbell-Hausdorff formula
- Jacobi and the birth of Lie's theory of groups
- An elementary proof of the Baker-Campbell-Hausdorff-Dynkin formula
- Subelliptic estimates and function spaces on nilpotent Lie groups
- Hypoelliptic differential operators and nilpotent groups
- On the convergence of exponential operators-the Zassenhaus formula, BCH formula and systematic approximants
- Quasinilpotent Banach-Lie algebras are Baker-Campbell-Hausdorff
- Goldberg's theorem and the Baker-Campbell-Hausdorff formula
- Emergence of the theory of Lie groups. An essay in the history of mathematics 1869--1926
- On the convergence and optimization of the Baker-Campbell-Hausdorff formula
- Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups
- Hypoelliptic second order differential equations
- A new proof of the Baker-Campbell-Hausdorff formula
- Explicit solution of the continuous Baker-Cambell-Hausdorff problem and a new expression for the phase operator
- Hilbert--Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry
- Die linearen Beziehungen zwischen höheren Kommutatoren
- A connection between the Baker-Hausdorff formula and a problem of Burnside
- A simple expression for the terms in the Baker–Campbell–Hausdorff series
- Convergence of the exponential Lie series
- Convergence domains for the campbell-baker-hausdorff formula
- Démonstration algébrique de la formule de Hausdorff
- Note on the Algebraic Aspect of the Integration of a System of Ordinary Linear Differential Equations
- Some properties of the campbell baker hausdorff series
- Splitting methods
- Pro-Lie groups which are infinite-dimensional Lie groups
- An efficient algorithm for computing the Baker–Campbell–Hausdorff series and some of its applications
- Dynkin’s method of computing the terms of the Baker–Campbell–Hausdorff series
- The Baker-Hausdorff Formula and a Problem in Crystal Physics
- Poincaré and Lie groups
- Cyclic Relations and the Goldberg Coefficients in the Campbell-Baker- Hausdorff Formula
- Lie series and invariant functions for analytic symplectic maps
- On the solution of linear differential equations in Lie groups
- Sur L'Intégrabilité des Sous–Algèbres de lie en Dimension Infinie
- Banach-Lie quotients, enlargibility, and universal complexifications
- Algebras whose groups of units are Lie groups
- Sophus Lie's Third Fundamental Theorem and the Adjoint Functor Theorem
- Maximal reductions in the Baker–Hausdorff formula
- Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
- Baker-Campbell-Hausdorff formulas
- Magnus and Fer expansions for matrix differential equations: the convergence problem
- The Baker–Campbell–Hausdorff formula and nested commutator identities
- The Baker-Campbell-Hausdorff formula and the convergence of the Magnus expansion
- Sufficient conditions for the convergence of the Magnus expansion
- Geometric Numerical Integration
- On Expanding the Exponential
- Perturbation Theory and Lie Algebras
- Note on the Global Validity of the Baker-Hausdorff and Magnus Theorems
- Expansion of the Campbell‐Baker‐Hausdorff formula by computer
- Properties of Higher-Order Commutator Products and the Baker-Hausdorff Formula
- Exponential Operators and Parameter Differentiation in Quantum Physics
- Normed Lie Algebras
- Mathematical aspects of the quantum theory of fields. Part V. Fields modified by linear homogeneous forces
- Lie groups
- The structure of compact groups. A primer for the student -- a handbook for the expert
