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arXiv · 1111.4271

Generalized Stieltjes transforms: basic aspects

Dmitry Karp·Elena Prilepkina
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Abstract

The paper surveys the basic properties of generalized Stieltjes functions including some new ones. We introduce the notion of the exact Stieltjes order and give a criterion of exactness, simple sufficient conditions and some prototypical examples. The paper includes an appendix, where we define the left sided Riemann-Liouville and the right sided Kober-Erdelyi fractional integrals of measures supported on half axis and give inversion formulas for them.

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Dmitry Karp, Elena Prilepkina. 2011-11-18. Generalized Stieltjes transforms: basic aspects. https://arxiv.org/abs/1111.4271

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