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On powers of Stieltjes moment sequences, II

Christian Berg
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Abstract

We consider the set of Stieltjes moment sequences, for which every positive power is again a Stieltjes moment sequence, we and prove an integral representation of the logarithm of the moment sequence in analogy to the Lévy-Khinchin representation. We use the result to construct product convolution semigroups with moments of all orders and to calculate their Mellin transforms. As an application we construct a positive generating function for the orthonormal Hermite polynomials.

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Christian Berg. 2004-12-17. On powers of Stieltjes moment sequences, II. https://arxiv.org/abs/math/0412340

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