Arnaud Denjoy

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Arnaud Denjoy (born January 5, 1884 in Auch im Département Gers ; † January 21, 1974 in Paris ) was a French mathematician who mainly worked in the field of real analysis .

life and work

Denjoy was the son of a Perpignan wine merchant and a Spanish mother. He attended the schools of Auch and Montpellier and studied from 1902 to 1905 at the École normal supérieure with Emile Picard , Émile Borel and Paul Painlevé and in 1905 acquired his agrégation in mathematics. Denjoy did so well as a student that he won a Thiers Foundation scholarship. Under the influence of Émile Borel and that of the writings of René Baire , he turned entirely to real analysis. After receiving his doctorate in 1909, he went to the University of Montpellier as a tutor (maître de conférence), a position previously held by René Baire. During the First World War he could not do active military service due to poor eyesight and in 1917 accepted a professorship in Utrecht , where Johannes van der Corput was his assistant. In 1919 he became a professor at the University of Strasbourg. In 1922 he became Chargé de Cours, in 1925 Maître de conférence and in 1931 Professor of General Mathematics at the Sorbonne in Paris (nominally on the chair of Celestial Mechanics previously occupied by Henri Poincaré ). From 1933 he held the chair for differential and integral calculus, and later for the theory of functions and topology. In 1955 he retired.

In a series of works from the 1920s onwards, he examined the calculation of the coefficients in convergent trigonometric series, summarized in a four-volume monograph that appeared from 1941 to 1949. This also includes one of his most famous discoveries, the Denjoy integral (first published in 1912), a generalization of the Riemann and Lebesgue integral, today with the theory of the integral partly named after Henstock, Kurzweil or Perron (in English also "Gauge Integral "called) fused. Other work by Denjoy concerned quasi-analytical functions. There Denjoy and Carleman's theorem is named after him, which specifies criteria for the fact that an analytic function is quasi-analytic (Denjoy 1921). Denjoy also made important contributions to the theory of dynamic systems , in particular to differential equations on the torus (Poincaré-Denjoy theory). The set of Denjoy (1932, Journal de Mathematiques) are criteria for when a diffeomorphism of a circle conjugate to a rotation. Denjoy and Wolff's theorem (additionally after Julius Wolff ) makes statements about fixed points of the iteration of holomorphic mappings of the open unit disk. In 1931 (Compte Rendus) Denjoy gave a probabilistic interpretation of the Riemann Hypothesis . From 1947 to 1954 he published a monograph on transfinite numbers.

Denjoy was friends with the Russian mathematician Nikolai Nikolajewitsch Lusin and had contacts with the mathematician from his school.

Denjoy was also politically active. He supported the radical party of the multiple French council president Édouard Herriot and was for this 1912 city councilor of Montpellier and from 1920 district administrator of the Gers department .

In 1939 he was elected to the American Academy of Arts and Sciences , in 1942 to the French Academy of Sciences . From 1962 he was its president. Denjoy was also a member of the Amsterdam, Warsaw and Liege Academies. In 1954 he was Vice President of the International Mathematical Union . In Russia, where he was in correspondence with Lusin, he was honored in 1970 with the Lomonosov gold medal. He had been a member of the Russian Academy of Sciences since 1971 . In 1950 he was invited speaker at the International Congress of Mathematicians (ICM) in Cambridge (Massachusetts) ( Les equations differentielles periodiques ). He also gave a lecture at the ICM in Strasbourg in 1920 ( Sur une classe d'ensembles parfaits en relation avec les fonctions admettant une dérivée seconde généralisée ). In 1931 he was president of the Société Mathématique de France .

He had been married since 1923 and had 3 sons.

The asteroid (19349) Denjoy was named after him.

See also

Fonts

  • Introduction a la théorie de fonctions de variables réelles, Volume 1, Hermann 1937
  • Aspects actuels de la pensée mathématique, Bulletin de la Société Mathématique de France, Volume 67, 1939, pp. 1-12 (supplément), numdam
  • Leçons sur le calcul des coefficients d'une série trigonométrique, 4 volumes, 1941–1949
  • L'énumération transfinie, 4 volumes, Gauthier-Villars, 1946–1954
  • Mémoire sur la dérivation et son calcul inverse, 1954, reprinted by Ed. Jacques Gabay
  • Articles et Mémoires, 2 volumes, 1955
  • Jubilé scientifique, 1956
  • Un demi-siècle de Notes académiques (1906–1956), 2 volumes, Gauthier-Villars, 1957 (collection of his essays)
  • Hommes, Formes et le Nombre, 1964

literature

  • Gustave Choquet , article Denjoy in Dictionary of Scientific Biography and in Asterisque Vol. 28/29, 1975.
  • Henri Cartan, Obituary in Comptes rendus de l'Académie des Sciences Paris, Vol. 279, 1974, pp. 49-53

Web links

Individual evidence

  1. ↑ Denjoy, Une extension de l'intégrale de M. Lebesgue, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences (Paris), Volume 154, 1912, pp. 859-862
  2. ^ Denjoy, Mémoire sur les nombres dérivés des fonctions continues, Journal de Mathématiques Pures et Appliquées, Series 7, Volume 1, 1915, pp. 105–240, online
  3. ↑ Generalizations of analytical functions, based on the transfer of the property of analytical functions in an interval that they vanish identically in the interval if the function and all its derivatives vanish at a point in the interval
  4. ↑ see e.g. B. Manfred Denker, Introduction to Analysis of Dynamic Systems , Springer-Verlag, 2005, p. 75, for the exact formulation and a proof.
  5. ↑ Denjoy-Wolff theorem, Encyclopedia of Mathematics, Springer
  6. ↑ Denjoy, L'énumeration transfini, Gauthier-Villars, 5 parts
  7. ^ Menschow Impressions sur mon voyage à Paris en 1927 , Cahiers du séminaire d'histoire des mathématiques, Vol. 6, 1985, pp. 55–59
  8. ^ Website Verlag Jacques Gabay on Denjoy with biography
personal data
SURNAME Denjoy, Arnaud
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH January 5, 1884
PLACE OF BIRTH Also , Département Gers
DATE OF DEATH January 21, 1974
Place of death Paris