Geodesic
On the Inversion of General Transformations*
Canadian mathematical bulletin, Tome 2 (1959) no. 1, pp. 19-24

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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. 
Rooney, P. G. On the Inversion of General Transformations*. Canadian mathematical bulletin, Tome 2 (1959) no. 1, pp. 19-24. doi: 10.4153/CMB-1959-005-3
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