International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 75816, 10 pages
doi:10.1155/IJMMS/2006/75816
Tauberian-type theorems with application to the Stieltjes
transformation
1Department of Mathematics, New Arts, Commerce and Science College Parner, Pune University, Pune, District Ahmednagar, 414302, Maharashtra, India
2Department of Mathematics, Shivaji University, Vidayanagar, Kolhapur 416004, Maharashtra, India
Received 22 November 2004; Revised 12 April 2006; Accepted 22 June 2006
Copyright © 2006 S. B. Gaikwad and M. S. Chaudhary. 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.
Abstract
In the first part, we define the space L'(r) and the modified Stieltjes transformation introduced by Lavoine and Misra (1979) and Marichev (1983), respectively. In the second part of the paper, we extend Tauberian-type theorems for the distributional Stieltjes transformations to the distributional modified Stieltjes transformations.