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 Poincaré 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) and quickly 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 the 20th
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.ovide 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 Poincaré 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) and quickly e
