A Representation Theorem for a Class of Stieltjes Transformable Generalized Functions

The classical Stieltjes transform has recently been extended to a certain class of generalized functions S_α' (I) by Pandey [1], and the real and complex inversion formulae [3, pp. 126, 144] have been shown to be still valid when the limiting operation in those formulae is understood as weak convergence in the space D'{I) of Schwartz distributions.