Paul 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 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.
In a paper of 1875, du Bois-Reymond employed for the first time the method of diagonalization, later associated with the name of Cantor.[1] 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 is also associated with the fundamental lemma of calculus of variations of which he proved a refined version based on that of Lagrange.[2][3]
Theory of infinitesimals
Paul du Bois-Reymond developed a theory of infinitesimals: Template:Pull quote
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)
References
<templatestyles src="Reflist/styles.css" />
- ↑ Script error: No such module "Citation/CS1".
- ↑ Dubois-Reymond: Erläuterungen zu den Anfangsgründen der Variationsrechnung. Mathematische Annalen, Band 15, 1879, S. 283–314, hier S. 297, 300.
- ↑ Oskar Bolza: Vorlesungen über Variationsrechnung. Teubner 1909, S. 26. Nach Bolza stammt der älteste Beweis von Friedrich Stegmann, Lehrbuch der Variationsrechnung, Kassel 1854, dort werden aber einschränkendere Annahmen gemacht.
Script error: No such module "Check for unknown parameters".
External links
- Template:Internet Archive author
- Script error: No such module "Template wrapper".
- Template:PAGENAMEBASE at the Mathematics Genealogy ProjectTemplate:EditAtWikidata
- Script error: No such module "citation/CS1".
Script error: No such module "Authority control".
- Pages with script errors
- Pages with broken file links
- 1831 births
- 1889 deaths
- 19th-century German mathematicians
- Mathematicians from Berlin
- People from the Province of Brandenburg
- Academic staff of the University of Freiburg
- Academic staff of the University of Tübingen
- Academic staff of Technische Universität Berlin
- German people of French descent
- Mathematicians from the Kingdom of Prussia
- Mathematicians from the German Empire