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Laurent Schwartz published the second part of his thesis in 1942 in the AFST. It is a methodical investigation of the Fourier analysis of functions generated by a sequence of complex exponentials. The first part of the thesis concerned the case of real exponentials. Both parts will be republished together in 1959. These fundamental results have become basic tools in harmonic analysis, in particular in the theory of Dirichlet series and trigonometric series. They have also been used recently in control theory (cf e.g. Glass, O., "A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit." J. Funct. Anal. 2010,  vol 258, no. 3, pp. 852-868)

The Annales de la Faculté des Sciences de Toulouse were founded in 1887 by H. Andoyer, B. Baillaud, G. Berson, T. Chauvin, E. Cosserat, A. Destrem, C. Fabre, A. Legoux, P. Sabatier, T.-J. Stieltjes. This multidisciplinary journal est exclusively dedicated to mathematics since 1979.
They publish high level articles and surveys, written in French or in English, in all fields of mathematics. There is no size restriction.
The Annales de la Faculté des Sciences de Toulouse is an Diamond open access journal since 2017 and is published with the support of CNRS, Université Paul Sabatier and l'Institut de Mathéamtique 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.