Files

memoria.pdf (381.11 KB)

Document type

Bachelor thesis

Publication date

2018-01-19

Publication license

cc-by-nc-nd (c) Miguel García Fernández, 2018
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/122536

Convergence and divergence of Fourier series

Journal Title

Authors

Director/Tutor

Additional contribution

Journal ISSN

Volume Title

Abstract

[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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: María Jesús Carro Rossell

Related resource

Subject

Sèries de Fourier, Treballs de fi de grau, Convergència (Matemàtica), Sumabilitat

Subject (English)

Fourier series, Bachelor's theses, Convergence, Sumabilitat

Citation

Collections

Treballs Finals de Grau (TFG) - Matemàtiques

Citation

GARCÍA FERNÁNDEZ, Miguel. Convergence and divergence of Fourier series. [consulted: 7 of October of 2026]. Available at: https://hdl.handle.net/2445/122536

Export metadata

JSON - METS

Share record