ABSTRACT
This chapter presents a quick review of the distribution theory. The principal importance of the Schwartz distributions as opposed to other distribution theories (more on those below) is that they are well-behaved under the Fourier transform. The Fourier transform of a Schwartz distribution is also a Schwartz distribution. The Schwartz distributions are the most convenient for Fourier transform theory. But the space D' is often more convenient in the theory of partial differential equations.
