Motivated by the importance of the Campbell, Baker, Hausdorff,
Dynkin Theorem in many different branches of Mathematics and
Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and
Statistical Mechanics, Numerical Analysis, Theoretical Physics,
Control Theory, sub-Riemannian Geometry), this monograph is
intended to: fully enable readers (graduates or specialists,
mathematicians, physicists or applied scientists, acquainted with
Algebra or not) to understand and apply the statements and numerous
corollaries of the main result, provide a wide spectrum of proofs
from the modern literature, comparing different techniques and
furnishing a unifying point of view and notation, provide a
thorough historical background of the results, together with
unknown facts about the effective early contributions by Schur,
Poincare, Pascal, Campbell, Baker, Hausdorff and Dynkin, give an
outlook on the applications, especially in Differential Geometry
(Lie group theory) and Analysis (PDEs of subelliptic type)
andquickly enable the reader, through a description of the
state-of-art and open problems, to understand the modern literature
concerning a theorem which, though having its roots in the
beginning of the20th century, has not ceased to provide new
problems and applications.
The book assumes some undergraduate-level knowledge of algebra
and analysis, but apart from that is self-contained. Part II of the
monograph is devoted to the proofs of the algebraic background. The
monograph may therefore provide a tool for beginners in
Algebra."
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