On two new characterizations of Steiltjes transforms for distributions - Sunil Kumar Sinha (International Journal of Mathematics and Mathematical Sciences)
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.