On powers of Stieltjes moment sequences. II (Q849601)
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scientific article; zbMATH DE number 5069025
| Language | Label | Description | Also known as |
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| English | On powers of Stieltjes moment sequences. II |
scientific article; zbMATH DE number 5069025 |
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On powers of Stieltjes moment sequences. II (English)
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31 October 2006
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The present paper is in continuation of the author's previous work [J. Theor. Probab. 18, 871--889 (2005; Zbl 1086.44003)]. Stieltjes characterized sequences by certain quadratic forms being non-negative. The author considers the set of Stieltjes moment sequences, for which every positive power is again a Stieltjes moment sequence. An integral representation of the logarithm of the moment sequence in analogy to the Levy-Khintchine representation is established. This result is used to construct product convolution semigroups with moments of all orders and to calculate their Mellin transforms. A positive generating function for orthonormal Hermite polynomials is obtained.
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infinite divisibility
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convolution semigroup
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\(q\)-series
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Hermite polynomials
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Stieltjes moment sequences
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Mellin transforms
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generating function
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