Paul David Gustav du Bois-Reymond

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Paul David Gustav du Bois-Reymond (December 2, 1831 – April 7, 1889) was a German mathematician who was born in Berlin and died in Freiburg. He was the brother of Emil du Bois-Reymond.

His thesis was concerned with the mechanical equilibrium of fluids. He worked on the theory of functions and in mathematical physics. His interests included Sturm-Liouville theory, integral equations, variational calculus, and Fourier series. In this latter field, he was able in 1876 to construct a continuous function whose Fourier series is not convergent.

Du Bois-Reymond also established that a trigonometric series that converges to a continuous function is the Fourier series of this function.

[edit] Writings

Théorie générale des fonctions (Nice : Impr. niçoise, 1887) (translated in French from the original German by G. Millaud and A. Girot)
De Aequilibrio Fluidorum (PhD Thesis, 1859)