International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 1, Pages 67-88

Abelian theorems for the stieltjes transform of functions, II

Richard D. Carmichael and Elmer K. Hayashi

Department of Mathematics, Wake Forest University, Winston-Salem 27109, North Carolina, USA

Received 18 April 1980

Copyright © 1981 Richard D. Carmichael and Elmer K. Hayashi. 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.


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.