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Springer Verlag, Mediterranean Journal of Mathematics, 2(11), p. 315-327
DOI: 10.1007/s00009-013-0311-z
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Levy-Khintchine Representations of the Weighted Geometric Mean and the Logarithmic Mean
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Abstract
The authors introduce the concept “degree of a complete Bernstein function”, establish Lévy-Khintchine representations of the weighted geometric mean and the logarithmic mean by the Cauchy integral formula, and obtain that the weighted geometric mean and the logarithmic mean are complete Bernstein functions of degree 0.