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, mathematical structure, structure, space, Mathematica ...
.
Biography
Denjoy was born in
Auch
Auch (; ) is a Communes of France, commune in southwestern France. Located in the Regions of France, region of Occitania (administrative region), Occitanie, it is the capital of the Gers Departments of France, department.
Geography
Localiza ...
,
Gers
Gers (; or , ) is a departments of France, department in the regions of France, region of Occitania (administrative region), Occitania, Southwestern France. Gers is bordered by the departments of Hautes-Pyrénées and Pyrénées-Atlantiques to ...
. His contributions include work in
harmonic analysis
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded do ...
and
differential equations.
His integral was the first to be able to integrate all
derivative
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is t ...
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 creat ...
. 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
Groupe Lactalis S.A. (doing business as 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 S.A.
Lactalis is the largest dairy pr ...
. In 1942 he was elected a member of the
Académie des sciences
The French Academy of 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 method, scientific research. It was at the forefron ...
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)
* Denjoy integral (disambiguation)
* Denjoy–Luzin theorem
* Denjoy–Luzin–Saks theorem
* 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 st ...
* 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, an ...
* Denjoy–Carleman theorem
* Denjoy–Carleman–Ahlfors theorem
* Denjoy's theorem on rotation number
* 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