3. Distributions

We will only give here the essential aspects of distribution theory, which are necessary for the theory of harmonic analysis; some important but difficult mathematical points, such as the exact description of the topology of the space $\mathcal{D}$ , have been deliberately omitted. Similarly, although the theory can be performed on any open of the space ${ℝ}^N$ , we will restrict ourselves to the case of the whole space, which is the only one that is really useful in the case of harmonic analysis.