Published online by Cambridge University Press: 20 November 2018
Let k be the kernel of a “general transformation”; that is, k(x) / x ϵ L2 (0,∞), and if x and y are positive
1
Then it is well known (see for example [8; Theorems 129 and 131]) that if the transform of fϵL2 (0,∞) is g, that is, if
2
then the inverse transform is given by
3
In practice, the inversion formula (3) is often hard to use. For example, the integral may be too difficult to evaluate; moreover, since (2) requires a differentiation, it is not well suited for numerical calculation. Hence it seems worthwhile to find other methods for inverting the transformation.
This paper was written while the author was a fellow at the 1958 Summer Research Institute of the Canadian Mathematical Congress, Kingston, Ontario.