Distributional Abelian theorems for the generalized Stieltjes transform (Q1096137)

The authors define a generalized Stieltjes transform of the type \[ F(s)=\int^{\infty}_{0}s^{-1}K(ts)f(t)dt, \] where the kernel K is a special case of the H-function first defined by \textit{C. Fox} [Trans. Am. Math. Soc. 98, 395-429 (1961; Zbl 0096.308)] and later modified by \textit{K. C. Gupta} [Ann. Soc. Sci. Bruxelles, I. Ser. 79, 97-106 (1965; Zbl 0128.336)] to the form used here. The paper is essentially comprised of Abelian theorems relating the behavior of functions F(s) to that of f(t) which are then extended to a certain class of generalized functions. In the concluding section, the authors relate distributional solutions of two initial boundary value problems discussed earlier by \textit{J. W. Dettman} [J. Math. Anal. Appl. 25, 341-349 (1969; Zbl 0169.432)] using their distributional transforms.