Generalized Stieltjes transforms: basic aspects

Details Generalized Stieltjes transforms: basic aspects Generalized Stieltjes transforms: basic aspects

2011-11-18

arxiv.org/abs/1111.4271v2

Mathematics

Classical Analysis and ODEs

23 pages, no figures; a counterexample related to complex variable chracterization added; some typos corrected, other minore i

Scientific paper

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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