After elaborating the integral that now bears his name, Henri Lebesgue has been studying the convergence of Fourier series in the early XXth century. In a series of articles, among which one is published in 1909 in the Annales de la Faculté des Sciences de Toulouse, Lebesgue analyzes approximations of unity (in modern language). He obtains several uniform convergence results of Fourier series, for instance for Lipschitz functions or more generally for Dini-Lipschitz functions, but he also obtains divergence results : Fourier series of a continuous function that does not converge everywhere (the first example is due to du Bois-Reymond), or Fourier series of a continuous function that converges everywhere but not uniformly.
Lebesgue's work was later extended by several striking results related to the convergence of Fourier series, the subject being still very active.
The Annales de la Faculté des Sciences de Toulouse was founded in 1887 by Andoyer, Baillaud, Berson, Chauvin, Cosserat, Destrem, Fabre, Legoux, Sabatier and Stieltjes. This multidisciplinary journal has been exclusively dedicated to mathematics since 1979. It publish high level articles and surveys, written in French or in English, in all areas of mathematics. There is no size restriction.
The Annales de la Faculté des Sciences de Toulouse has been a Diamond open access journal since 2017. It is published with the support of CNRS, Université Paul Sabatier and the Institut de Mathématiques de Toulouse.
This journal, previously hosted by Cedram, is now web-published by the Centre Mersenne. In 2019, Cedram has become the Centre Mersenne for open scientific publishing, a publishing platform for scientific journals developed by Mathdoc.