Convergence and divergence of Fourier series

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: María Jesús Carro Rossell[en] In this project we study the convergence of Fourier series. Specifically, we first give some positive results about pointwise and uniform convergence, and then we prove two essential negative results: there exists a continuous function whose Fourier series diverges at some point and an integrable function whose Fourier series diverges almost at every point. In the case of divergence, we show that one can use other summability methods in order to represent the function as a trigonometric series