International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 677-685

Abelian theorem for the Stieltjes transform of distributions

Bogoljub Stanković

Institute of Mathematics, University of Novi Sad, Serbia

Received 13 February 1989; Revised 15 March 1989

Copyright © 1990 Bogoljub Stanković. 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.


First, a definition is given of the Stieltjes transform of distributions which contains some well-known. Then, a structural theorem for distributions having S-asymptotic is proved. This makes possible to prove two theorems of the Abelian type valued for Stieltjes transforms of distributions given in different ways.