Arnaud Denjoy (; 5 January 1884 – 21 January 1974) was a French
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
.
Biography
Denjoy was born in
Auch
Auch (; oc, label= Gascon, Aush ) is a commune in southwestern France. Located in the region of Occitanie, it is the capital of the Gers department. Auch is the historical capital of Gascony.
Geography
Localization
Hydrography
The Riv ...
,
Gers
Gers (; oc, Gers or , ) is a department in the region of Occitania, Southwestern France. Named after the Gers River, its inhabitants are called the ''Gersois'' and ''Gersoises'' in French. In 2019, it had a population of 191,377. . His contributions include work in
harmonic analysis
Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fo ...
and
differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s.
His integral was the first to be able to integrate all
derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. F ...
s. Among his students is
Gustave Choquet
Gustave Choquet (; 1 March 1915 – 14 November 2006) was a French mathematician.
Choquet was born in Solesmes, Nord. His contributions include work in functional analysis, potential theory, topology and measure theory. He is known for creati ...
. He is also known for the more general
broad Denjoy integral, or Khinchin integral.
Denjoy was an Invited Speaker of the
ICM with talk ''Sur une classe d'ensembles parfaits en relation avec les fonctions admettant une dérivée seconde généralisée'' in 1920 at Strasbourg and with talk ''Les equations differentielles periodiques'' in 1950 at Cambridge, Massachusetts. In 1931 he was the president of the
Société Mathématique de France. In 1942 he was elected a member of the
Académie des sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the ...
and was its president in 1962.
Denjoy married in 1923 and was the father of three sons. He died in Paris in 1974. He was an atheist with a strong interest in philosophy, psychology, and social issues.
The asteroid
(19349) Denjoy is named in his honor.
Selected publications
''Une extension de l'intégrale de Lebesgue'', Académie des Sciences, pp. 859–862 (1912)''Les continus cycliques et la représentation conforme'', Bulletin de la Société Mathématique de France, pp. 97-124 (1942)''Sur les fonctions dérivées sommables.'', Bulletin de la Société Mathématique de France, pp. 161-248 (1915)
*Introduction à la théorie de fonctions de variables réelles, vol. 1, Hermann 1937
*Aspects actuels de la pensée mathématique, Bulletin de la Société Mathématique de France, vol. 67, 1939, pp. 1–12 (supplément)
numdam
*Leçons sur le calcul des coefficients d'une série trigonométrique, 4 vols., 1941–1949
*L'énumération transfinie, 4 vols., Gauthier-Villars, 1946–1954
*Mémoire sur la dérivation et son calcul inverse, 1954, published by Éditions Jacques Gabaywebsite of publishing company Éditions Jacques Gabay with brief biography of Denjoy
/ref>
*Articles et Mémoires, 2 vols., 1955
*Jubilé scientifique, 1956
*Un demi-siècle de Notes académiques (1906–1956), 2 vols., Gauthier-Villars, 1957 (collection of Denjoy's essays)
*Hommes, Formes et le Nombre, 1964
See also
* Denjoy theorem (disambiguation) In mathematics, Denjoy's theorem may refer to several theorems proved by Arnaud Denjoy, including
* Denjoy–Carleman theorem
* Denjoy–Koksma inequality
* Denjoy–Luzin theorem
* Denjoy–Luzin–Saks theorem
* Denjoy–Riesz theorem
* Denj ...
* Denjoy integral (disambiguation) The Denjoy integral in mathematics can refer to two closely related integrals connected to the work of Arnaud Denjoy:
* the ''narrow'' Denjoy integral, or just Denjoy integral, also known as Henstock–Kurzweil integral,
* the (more general) ''wi ...
* Denjoy–Luzin theorem
* Denjoy–Luzin–Saks theorem
In mathematics, the Denjoy–Luzin–Saks theorem states that a function of generalized bounded variation in the restricted sense has a derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to ...
* Denjoy–Riesz theorem
* Denjoy–Young–Saks theorem
* Denjoy–Carleman theorem
* Denjoy–Carleman–Ahlfors theorem The ''Denjoy–Carleman–Ahlfors theorem'' states that the number of asymptotic values attained by a non-constant entire function of order ρ on curves going outwards toward infinite absolute value is less than or equal to 2ρ. It was first conjec ...
* Denjoy's theorem on rotation number
In mathematics, the Denjoy theorem gives a sufficient condition for a diffeomorphism of the circle to be topologically conjugate to a diffeomorphism of a special kind, namely an irrational rotation. proved the theorem in the course of his topolog ...
* Denjoy–Koksma inequality In mathematics, the Denjoy–Koksma inequality, introduced by as a combination of work of Arnaud Denjoy and the Koksma–Hlawka inequality of Jurjen Ferdinand Koksma, is a bound for Weyl sums \sum_^f(x+k\omega) of functions ''f'' of bounded varia ...
* Denjoy–Wolff theorem
In mathematics, the Denjoy–Wolff theorem is a theorem in complex analysis and dynamical systems concerning fixed points and iterations of holomorphic mappings of the unit disc in the complex numbers into itself. The result was proved independen ...
References
External links
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1884 births
1974 deaths
People from Auch
French atheists
20th-century French mathematicians
École Normale Supérieure alumni
Members of the French Academy of Sciences
Foreign Members of the USSR Academy of Sciences
Recipients of the Lomonosov Gold Medal
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