International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, pp. 3233

Given a distribution S on and an infinitely differentiable multiplier function α, the division problem consists in finding a distribution T such that .
If α never vanishes, is the unique answer. If , and if α has only isolated zeros of finite order, it can be reduced to a collection of cases where the multiplier is , for which the general solution can be shown to be of the formwhere U is a particular solution of the division problem and the are arbitrary constants.
In dimension , the problem is much more difficult, but is of fundamental importance in the theory of linear partial differential equations, since the Fourier transformation turns the problem of solving these into a division problem for distributions [see Hörmander (1963)].
References
Hörmander, L. (1963). Linear Partial Differential Operators. Berlin: SpringerVerlag.