In this paper we treat the problem of resonance absorption in isolated Breit-Wigner resonances of an absorber in an infinite homogeneous mixture of the absorber and moderator with an explicit treatment of the moderator collision integral. It is shown that Fourier transform techniques can profitably be used to treat this problem. However, the treatment calls for certain ideas from the theory of distributions similar to those used by Case in singular eigenfunction theory. The formulation leads to Fredholm integral equations in the transform variable whose solution gives the integral parameter of interest, namely, the effective resonance integral directly. In the limit of zero temperature, we obtain a second-order differential equation in the transform variable and formulate an accurate and fast converging iterative scheme to extract the resonance integral from its solution. Explicit formulas are derived for the resonance integral including the effect of resonance potential interference scattering. The analysis also provides an analytical expression for the asymptotic flux distribution well below the resonance energy. Numerical results are presented to demonstrate the accuracy of the method.