Richard D. Carmichael, Elmer K. Hayashi, "Abelian theorems for the stieltjes transform of functions, II", International Journal of Mathematics and Mathematical Sciences, vol. 4, Article ID 863151, 22 pages, 1981. https://doi.org/10.1155/S0161171281000045
Abelian theorems for the stieltjes transform of functions, II
An initial (final) value Abelian theorem concerning transforms of functions is a result in which known behavior of the function as its domain variable approaches zero (approaches ) is used to infer the behavior of the transform as its domain variable approaches zero (approaches ). We obtain such theorems in this paper concerning the Stieltjes transform. In our results all parameters are complex; the variable of the transform is complex in the right half plane; and the initial (final) value Abelian theorems are obtained as within an arbitrary wedge in the right half plane.
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