The geometric mean is a Bernstein function
arXiv:1301.6848 · doi:10.7153/mia-17-53
Abstract
In the paper, the authors establish, by using Cauchy integral formula in the theory of complex functions, an integral representation for the geometric mean of $n$ positive numbers. From this integral representation, the geometric mean is proved to be a Bernstein function and a new proof of the well known AG inequality is provided.
10 pages