On Certain Dual Integral Equations

Abstract

In his book on Fourier Integrals, Titchmarsh [l] gave the solution of the dual integral equations for the case α > 0, by some difficult analysis involving the theory of Mellin transforms. Sneddon [2] has recently shown that, in the cases v = 0, α = ±½, the problem can be reduced to an Abel integral equation by making the substitution or It is the purpose of this note to show that the general case can be dealt with just as simply by putting The analysis is formal: no attempt is made to supply details of rigour.