December 02, 2014 <Back to Index>
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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 1873 to construct a continuous function whose Fourier series is not convergent. His lemma defines a sufficient condition to guarantee that a function vanishes almost everywhere. 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. He developed a theory of infinitesimals in Über die Paradoxen des Infinitär - Calcüls ("On the paradoxes of the infinitary calculus") in 1877. He writes:-
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