Some “Short” Proofs of the CBHD Theorem
2011; Springer Nature; Linguagem: Inglês
10.1007/978-3-642-22597-0_4
ISSN1617-9692
AutoresAndrea Bonfiglioli, Roberta Fulci,
Tópico(s)Polynomial and algebraic computation
ResumoTHE 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.
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