Fourier Analysis


In this course we present some fundamental properties of the Fourier series and the Fourier transform. Starting with remarks on the convolution (and its different behaviors on the real line or on the torus) we introduce the Fourier series using kernels. After identifying the properties of the Dirichlet kernel and the Féjer kernel we present a more hilbertian approach to the subject and restrict ourselves to the study of square-integrable functions over the torus. We use this tools to analyze the heat equation over the torus. We then introduce the Fourier transform over the real line for integrable function and its extension to square integrable function. After some applications we conclude by drawing a link with distributions.
This course was written by my predecessor Arthur Leclaire.


  • Analyse numérique et optimisation (Allaire)


Cours d’analyse de Fourier