English

On powers of Stieltjes moment sequences, II

Classical Analysis and ODEs 2007-05-23 v1 Complex Variables

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 L\'evy-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.

Keywords

Cite

@article{arxiv.math/0412340,
  title  = {On powers of Stieltjes moment sequences, II},
  author = {Christian Berg},
  journal= {arXiv preprint arXiv:math/0412340},
  year   = {2007}
}

Comments

preprint, 21 pages