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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 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.