When a function ofr, the absolute value of the distance between two points, falls off so slowly that not all its moments exist, then the decay of the function at largercan be related to the behavior of its threehyphen;dimensional Fourier transform at smallk. These results are extended to functionsFlpar;r1, r2, r3rpar;of the three relative distances between three points. The behavior ofFfor larger1, r2, r3is related to the behavior of the sixhyphen;dimensional Fourier transform for smallk1, k2, k3. We treat a class of functions which asymptotically become homogeneous inr1, r2,andr3. The dependence on the degree of homogeneity is considered in detail. The results can be applied to the convolutionhyphen;type integral equations which arise in statistical mechanics.
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