Mathematician:Paul David Gustav du Bois-Reymond

Mathematician
German mathematician who worked on the mechanical equilibrium of fluids, the theory of functions and in mathematical physics.

Also worked on Sturm–Liouville theory, integral equations, variational calculus, and Fourier series.

In $1873$, constructed a continuous function whose Fourier series is not convergent.

His lemma defines a sufficient condition to guarantee that a function vanishes almost everywhere.

Also established that a trigonometric series that converges to a continuous function at every point is the Fourier series of this function.

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 Lagrange.

Nationality
German

History

 * Born: 2 December 1831 in Berlin, Germany
 * Died: 7 April 1889 in Freiburg, Germany

Theorems and Definitions

 * Du Bois-Reymond Constants

Publications

 * 1853: De Aequilibrio Fluidorum (Ph.D thesis)
 * 1864: Beiträge zur Interpretation der partiellen Differentialgleichungen mit drei Variabeln
 * 1871: Notiz über einen Cauchy'schen Satz, die Stetigkeit von Summen unendlicher Reihen betreffend
 * 1871: Die Theorie der Fourier'schen Integrale und Formeln
 * 1873: Eine neue Theorie der Convergenz und Divergenz von Reihen mit positiven Gliedern
 * 1876: Zusätze zur Abhandlung: Untersuchungen über die Convergenz und Divergenz der Fourier'schen Darstellungsformeln
 * 1876: Notiz über infinitäre Gleichheiten
 * 1877: Über die Paradoxen des Infinitär-Calcüls ("On the paradoxes of the infinitary calculus")
 * 1877: Zwei Sätze über Grenzwerthe von Functionen zweier Veränderlichen
 * 1877: Note über die Integration totaler Differentialgleichungen
 * 1878: Notiz über Convergenz von Integralen mit nicht verschwindendem Argument
 * 1879: Über Integration und Differentiation infinitärer Relationen
 * 1879: Über Integration und Differentiation infinitärer Relationen

Also known as
Some sources omit the hyphen: du Bois Reymond.

Some sources render the name as Du Bois Raymond, but it is not clear whether that is a mistake or merely an alternative rendering.