Lars Edvard Phragmén (2 September 1863
Örebro – 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 then
Stockholm
Stockholm () is the Capital city, capital and List of urban areas in Sweden by population, largest city of Sweden as well as the List of urban areas in the Nordic countries, largest urban area in Scandinavia. Approximately 980,000 people liv ...
, graduating from Uppsala in 1889. He became professor at Stockholm in 1892, after
Sofia Kovalevskaia.
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.
His work focused on
elliptic function
In the mathematical field of complex analysis, elliptic functions are a special kind of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Originally those in ...
s and
complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...
. 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
Ernst is both a surname and a given name, the German, Dutch, and Scandinavian form of Ernest. Notable people with the name include:
Surname
* Adolf Ernst (1832–1899) German botanist known by the author abbreviation "Ernst"
* Anton Ernst (1975- ...
. 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.
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
''Acta Mathematica'' is a peer-reviewed open-access scientific journal covering research in all fields of mathematics.
According to Cédric Villani, this journal is "considered by many to be the most prestigious of all mathematical research journ ...
''. He is also famous for having pointed out (at 26) an unclear part of
Henri Poincaré
Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
's preprint on the
three-body problem. This led Poincaré to discover a major mistake in his own work, paving the way to important developments in
chaos theory
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have co ...
.
In addition to analysis, Phragmén was interested in the mathematics underlying insurance companies, and voting.
See also
*
Phragmen–Brouwer theorem
*
Phragmen-Lindelof principle
*
Phragmen's voting rules
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