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# Paul David Gustav du Bois-Reymond

Paul David Gustav du Bois-Reymond (2 December 1831 – 7 April 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 at every point is the Fourier series of this function.

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)

External links

* O'Connor, John J.; Robertson, Edmund F., "Paul David Gustav du Bois-Reymond", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Du_Bois-Reymond.html .

* Paul David Gustav du Bois-Reymond at the Mathematics Genealogy Project

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