International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 719-723
doi:10.1155/S0161171285000801
On two new characterizations of Stieltjes transforms for distributions
Sunil Kumar Sinha
Department of Mathematics, Tata College Chaibasa, Singhbhum, Bihar 833202, India
Abstract
Two new characterizations of the Stieltjes transform for distribution are developed, using two transformations on the space of distributions viz., dilation Un and exponential shifts T−p. The standard theorem on analyticity, uniqueness and invertibility of the Stieltjes transform are proved, using the new characterization as the definition of the Stieltjes transform.