Paul du Bois-Reymond (nonfiction): Difference between revisions
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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 also discovered a proof method that later became known as the [[Cantor's diagonal argument (nonfiction)|Cantor's diagonal argument]]. | 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 also discovered a proof method that later became known as the [[Cantor's diagonal argument (nonfiction)|Cantor's diagonal argument]]. | ||
His name is also associated with the fundamental lemma of calculus of variations of which he proved a refined version based on that of Lagrange. | His name is also associated with the fundamental lemma of calculus of variations of which he proved a refined version based on that of [[Joseph-Louis Lagrange (nonfiction)|Joseph-Louis Lagrange]]. | ||
== In the News == | == In the News == | ||
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* [[Cantor's diagonal argument (nonfiction)]] | * [[Cantor's diagonal argument (nonfiction)]] | ||
* [[Fourier series (nonfiction)]] | * [[Fourier series (nonfiction)]] | ||
* [[Joseph-Louis Lagrange (nonfiction)]] | |||
* [[Mathematician (nonfiction)]] | * [[Mathematician (nonfiction)]] | ||
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* [https://en.wikipedia.org/wiki/Paul_du_Bois-Reymond Paul du Bois-Reymond] @ Wikipedia | * [https://en.wikipedia.org/wiki/Paul_du_Bois-Reymond Paul du Bois-Reymond] @ Wikipedia | ||
[[Category:Nonfiction (nonfiction)]] | [[Category:Nonfiction (nonfiction)]] | ||
[[Category:Mathematicians (nonfiction)]] | [[Category:Mathematicians (nonfiction)]] | ||
[[Category:People (nonfiction)]] | [[Category:People (nonfiction)]] | ||
[[Category:Portraits (nonfiction)]] | |||
Revision as of 17:48, 14 November 2017
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 also discovered a proof method that later became known as the Cantor's diagonal argument.
His name is also associated with the fundamental lemma of calculus of variations of which he proved a refined version based on that of Joseph-Louis Lagrange.
In the News
Fiction cross-reference
Nonfiction cross-reference
- Cantor's diagonal argument (nonfiction)
- Fourier series (nonfiction)
- Joseph-Louis Lagrange (nonfiction)
- Mathematician (nonfiction)
External links:
- Paul du Bois-Reymond @ Wikipedia