An inversion theorem for the Stieltjes transform of distributions

Abstract

The Stieltjes transformation of generalized functions was investigated by Benedetto[1], Zemanian [16], Misra [10] Pandey [11], Lavoine and Misra [7], and Erdélyi [5]. The inversion theorems for the Stieltjes transform of generalized functions, in their own approaches, were given in Benedetto [1], Zemanian [16], Pandey [11], Pathak [12] (he used Pande's approach) and Erdélyi [5].