Pierre Fatou | |
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| Born | (1878-02-28)28 February 1878 Lorient, France |
| Died | 9 August 1929(1929-08-09) (aged 51) Pornichet, France |
| Alma mater | École Normale Supérieure |
| Known for | |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Paris Observatory |
| Doctoral advisor | Paul Painlevé |
Pierre Joseph Louis Fatou (28 February 1878 – 9 August 1929[1]) was a French mathematician andastronomer. He is known for major contributions to several branches ofanalysis. TheFatou lemma and theFatou set are named after him.
Pierre Fatou's parents were Prosper Ernest Fatou (1832-1891) and Louise Eulalie Courbet (1844-1911), both of whom were in the military.[1] Pierre's family would have liked for him to enter the military as well, but his health was not sufficiently good for him to pursue a military career.[1]
Fatou entered theÉcole Normale Supérieure in Paris in 1898 to study mathematics and graduated in 1901 when he was appointed an intern (stagiaire) in theParis Observatory. Fatou was promoted to assistant astronomer in 1904 and to astronomer (astronome titulaire) in 1928. He worked in this observatory until his death.
Fatou was awarded theBecquerel prize in 1918; he was a knight of theLegion of Honour (1923).[2] He was the president of theFrench mathematical society in 1927.[3]
He was in friendly relations with several contemporary French mathematicians, especially,Maurice René Fréchet andPaul Montel.[4]
In the summer of 1929 Fatou went on holiday to Pornichet, a seaside town to the west of Nantes. He was staying in Le Brise-Lames Villa near the port and it was there at 8 p.m. on Friday 9 August that he died in his room.[1] No cause of death was given on the death certificate but Audin argues that he died as a result of a stomach ulcer that burst. Fatou's nephew Robert Fatou wrote:
Having never thought it useful during his life to consult a doctor, my dear uncle died suddenly in a hotel room in Pornichet.
— Pierre Joseph Louis Fatou,[1]
Fatou's funeral was held on 14 August in the church of Saint-Louis, and he was buried in the Carnel Cemetery in Lorient.[1]
Fatou's work had very large influence on the development ofanalysis in the 20th century.
Fatou's PhD thesisSéries trigonométriques et séries de Taylor (Fatou 1906) was the first application of theLebesgue integral to concrete problems ofanalysis, mainly to the study of analytic and harmonic functions in the unit disc. In this work, Fatou studied for the first time thePoisson integral of an arbitrarymeasure on the unit circle. This work of Fatou is influenced byHenri Lebesgue who invented his integral in 1901.
TheFatou theorem, which says that a boundedanalytic function in the unit disc has radial limitsalmost everywhere on the unit circle was published in 1906 (Fatou 1906). This theorem was at the origin of a large body of research in 20th-century mathematics under the name ofbounded analytic functions.[5] See also the Wikipedia article on functions ofbounded type.
A number of fundamental results on theanalytic continuation of aTaylor series belong to Fatou.[6]
In 1917–1920 Fatou created the area of mathematics which is calledholomorphic dynamics (Fatou 1919,1920,1920b). It deals with a global study of iteration of analytic functions. He was the first to introduce and study the set which is called now theJulia set.[citation needed] (The complement of this set is sometimes called theFatou set). Some of the basic results of holomorphic dynamics were also independently obtainedbyGaston Julia and Samuel Lattes in 1918.[7] Holomorphic dynamics has experienced a strong revival since 1982 because of the new discoveries ofDennis Sullivan,Adrien Douady,John Hubbard and others. In 1926, Fatou pioneered the study of dynamics oftranscendentalentire functions (Fatou 1926), a subject which isintensively developing at this time.
As a byproduct of his studies in holomorphic dynamics, Fatou discovered what are now calledFatou–Bieberbach domains (Fatou 1922). These are proper subregions of the complex space of dimensionn, which are biholomorphically equivalent to the whole space. (Such regions cannot exist forn=1.)
Fatou did important work incelestial mechanics. He was the first to prove rigorously[8] a theorem (conjectured byGauss) on the averaging of aperturbation produced by a periodic force of short period (Fatou 1928). This work was continued byLeonid Mandelstam andNikolay Bogolyubov and his students and developed into a large area of modern applied mathematics. Fatou's other research in celestial mechanics includes a study of the movement of a planet in a resisting medium.(Fatou 1923b)
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