Fourier series development
Functional transformations

The method of Fourier series development, which is already quite old, is used in many problems that naturally involve periodicity (problems relating to crystals, lattices), we can also make periodicity appear in angles, by switching to polar coordinates. We can also transform a problem into a parallelepipedic domain Ω, making it periodic, to make precise use of Fourier series developments.

Let $\mathbb{T}$ be the unit circle of the complex plane $ℂ$; this set is identified with the quotient...