Recent developments on the Stieltjes transform of generalized functions (Q1098064)

This is a survey on recent developments of the Stieltjes transform of generalized functions. Definitions by means of the kernel method and by means of the method of adjoints, real and complex inversion theorems, representation of the Stieltjes transform as iterated Laplace transform, iterated Stieltjes transforms, Stieltjes transforms of higher order and the connection of such transforms of different order by means of fractional integration, further generalizations with the Gaussian hypergeometric function in the kernel, Abelian theorems are some important notions occuring in this article. Because of the range of the paper the informations are of course not complete.