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. 258 (2010), no. 3, 852-86.)