International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1981 / Article

Open Access

Volume 4 |Article ID 863151 | https://doi.org/10.1155/S0161171281000045

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

Received18 Apr 1980

Abstract

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 s of the transform is complex in the right half plane; and the initial (final) value Abelian theorems are obtained as |s|0(|s|) within an arbitrary wedge in the right half plane.

Copyright © 1981 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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