THE aim of this chapter is to give all the details of five other proofs (besides the one given in Chap. 3) of the Campbell, Baker, Hausdorff Theorem, stating that ; x♦y := Log(Exp(x) ·Exp(y)) is a series of Lie polynomials in x, y. As we showed in Chap. 3, this is the “qualitative” part of the CBHD Theorem, and the actual formula expressing xthat x♦y as an explicit series (that is, Dynkin’s Formula) can be quite easily derived from this qualitative counterpart as exhibited in Sect. 3.3.
CITATION STYLE
Bonfiglioli, A., & Fulci, R. (2012). Some “Short” proofs of the CBHD theorem. In Lecture Notes in Mathematics (Vol. 2034, pp. 173–264). Springer Verlag. https://doi.org/10.1007/978-3-642-22597-0_4
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