Convergence of Fourier series

Abstract

The main goal of this dissertation is to study the problem of convergence of Fourier series. This problem consists on, given a function f, deciding if its Fourier series converges to f. What conditions are necessary or sufficient for that to happen? What do we actually mean with convergence? We are going to give an answer to these question in this dissertation. The problem of convergence of Fourier series was first posed in the beginning of the XIX century, and it has evolved with the development if mathematical analysis. Several great mathematicians have worked on Fourier series, and this subject has in uenced some of them. It would be bold to say that Fourier series have shaped the development of history of mathematics, but there is no doubt that it has in uenced it in some way.