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,
Gers. His contributions include work in
harmonic analysis 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. ...
s. Among his students is
Gustave Choquet. 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
Lactalis is a French multinational dairy products corporation, owned by the Besnier family and based in Laval, Mayenne, France. The company's former name was Besnier SA.
Lactalis is the largest dairy products group in the world, and is the sec ...
. 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 th ...
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
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*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
* Denjoyâ ...
* Denjoy integral (disambiguation) The Denjoy integral in mathematics can refer to two closely related integrals connected to the work of Arnaud Denjoy
Arnaud Denjoy (; 5 January 1884 – 21 January 1974) was a French mathematician.
Biography
Denjoy was born in Auch, Gers. His co ...
* Denjoy–Luzin theorem
In mathematics, the Denjoy–Luzin theorem, introduced independently by and
states that if a trigonometric series converges absolutely on a set of positive measure, then the sum of its coefficients
In mathematics, a coefficient is a multi ...
* 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 almost everywhere
In measure theory (a branch of mathematical analysis), a property holds almos ...
* Denjoy–Riesz theorem
In topology, the Denjoy–Riesz theorem states that every compact set of totally disconnected points in the Euclidean plane can be covered by a continuous image of the unit interval, without self-intersections (a Jordan arc).
Definitions and sta ...
* Denjoy–Young–Saks theorem
In mathematics, the Denjoy–Young–Saks theorem gives some possibilities for the Dini derivatives of a function that hold almost everywhere.
proved the theorem for continuous functions, extended it to measurable function
In mathematics and ...
* Denjoy–Carleman theorem
* Denjoy–Carleman–Ahlfors theorem
* 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
* Denjoy–Wolff theorem
References
External links
*
*
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
{{France-mathematician-stub