Fourier transform
Functional analysis - Part 2

We have already come across some aspects of Fourier analysis (cf. article [ AF 100 , § 2]). In this section, we'll look at some applications of Fourier methods to the solution of partial differential equations. It should be remembered that J.B. Fourier was led to consider the series that bear his name when he sought (in his 1807 memoir) to solve the "heat equation".

We'll need the following notations.