Lars Edvard Phragmén (2 September 1863

Örebro Örebro ( , ) is the sixth-largest city in Sweden, the seat of Örebro Municipality, and capital of the Örebro County. It is situated by the Närke Plain, near the lake Hjälmaren, a few kilometers inland along the small river Svartån, and ...

– 13 March 1937) was a

Swedish Swedish or ' may refer to: Anything from or related to Sweden, a country in Northern Europe. Or, specifically: * Swedish language, a North Germanic language spoken primarily in Sweden and Finland ** Swedish alphabet, the official alphabet used by ...

mathematician. The son of a college professor, he studied at

Uppsala Uppsala (, or all ending in , ; archaically spelled ''Upsala'') is the county seat of Uppsala County and the fourth-largest city in Sweden, after Stockholm, Gothenburg, and Malmö. It had 177,074 inhabitants in 2019. Located north of the c ...

then Stockholm, graduating from Uppsala in 1889. He became professor at Stockholm in 1892, after

Sofia Kovalevskaia Sofya Vasilyevna Kovalevskaya (russian: link=no, Софья Васильевна Ковалевская), born Korvin-Krukovskaya ( – 10 February 1891), was a Russian mathematician who made noteworthy contributions to analysis, partial differen ...

. He left Uppsala less than a year after, becoming professor Mittag-Leffler's assistant at Stockholm. In 1884, he provided a new proof of the

Cantor-Bendixson theorem In descriptive set theory, a subset of a Polish space has the perfect set property if it is either countable or has a nonempty perfect subset (Kechris 1995, p. 150). Note that having the perfect set property is not the same as being a p ...

. His work focused on elliptic functions and complex analysis. His most famous result is the extension of Liouville's theorem to analytic functions on a sector. A first version was proposed by Phragmén, then improved by the Finnish mathematician Ernst Lindelöf. They jointly published this last version,« ''Sur une extension d'un principe classique de l'analyse et sur quelques propriétés des fonctions monogènes dans le voisinage d'un point singulier'' », Acta Math. 31, 1908 known as the

Phragmén–Lindelöf principle In complex analysis, the Phragmén–Lindelöf principle (or method), first formulated by Lars Edvard Phragmén (1863–1937) and Ernst Leonard Lindelöf (1870–1946) in 1908, is a technique which employs an auxiliary, parameterized function to ...

. He left the university in 1903, joining the Royal Inspection of Insurance Companies. He became director the following year. In 1908, he was appointed director of the insurance company Allmänna Lifförsakringsbolaget. From 1889 until his death, he was an active editor of '' Acta Mathematica''. He is also famous for having pointed out (at 26) an unclear part of Henri Poincaré's preprint on the

three-body problem In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's ...

. This led Poincaré to discover a major mistake in his own work, paving the way to important developments in chaos theory. In addition to analysis, Phragmén was interested in the mathematics underlying insurance companies, and voting.

References

* Yngve Domar, « Mathematical research during the first decades of the University of Stockholm », Stockholm University, 1978 (written and translated by H. Troy and H.S. Shapiro)

External links

Biography
{{DEFAULTSORT:Phragmen, Lars Swedish mathematicians Academic staff of Stockholm University Members of the Royal Swedish Academy of Sciences 1863 births 1937 deaths

See also

References

External links