International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 14, Article ID 75816, 10 pages
doi:10.1155/IJMMS/2006/75816
Tauberian-type theorems with application to the Stieltjes transformation
S.B. Gaikwad1
and M.S. Chaudhary2
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
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.