Lars Edvard Phragmén
Encyclopedia
Lars Edvard Phragmén was a Swedish
mathematician.
The son of a college professor, he studied at Uppsala
then Stockholm
, graduating 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 provides a new proof of the Cantor-Bendixson theorem.
His works focus on elliptic function
s and complex analysis
. His most famous result is the extension of Liouville's theorem
to bounded
entire function
s. A first version was proposed by Phragmén, then improved by the Finnish topologist Ernst Lindelöf
. They jointly published this last version , known as the Phragmén–Lindelöf principle.
He leaves 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. This lead Poincaré to discover a major mistake in his own work, paving the way to the important developments in chaos theory
.
Calculus aside, Phragmén was interested in the mathematics underlying insurance companies, and voting.
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....
mathematician.
The son of a college professor, he studied at Uppsala
Uppsala University
Uppsala University is a research university in Uppsala, Sweden, and is the oldest university in Scandinavia, founded in 1477. It consistently ranks among the best universities in Northern Europe in international rankings and is generally considered one of the most prestigious institutions of...
then Stockholm
Stockholm University
Stockholm University is a state university in Stockholm, Sweden. It has over 28,000 students at four faculties, making it one of the largest universities in Scandinavia. The institution is also frequently regarded as one of the top 100 universities in the world...
, graduating 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 provides a new proof of the Cantor-Bendixson theorem.
His works focus on elliptic function
Elliptic function
In complex analysis, an elliptic function is a function defined on the complex plane that is periodic in two directions and at the same time is meromorphic...
s and complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
. His most famous result is the extension of Liouville's theorem
Liouville's theorem
Liouville's theorem has various meanings, all mathematical results named after Joseph Liouville:*In complex analysis, see Liouville's theorem ; there is also a related theorem on harmonic functions....
to bounded
Bounded function
In mathematics, a function f defined on some set X with real or complex values is called bounded, if the set of its values is bounded. In other words, there exists a real number M...
entire function
Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic over the whole complex plane...
s. A first version was proposed by Phragmén, then improved by the Finnish topologist Ernst Lindelöf
Ernst Leonard Lindelöf
Ernst Leonard Lindelöf, was a Finnish topologist after whom Lindelöf spaces are named; he was the son of Leonard Lorenz Lindelöf and brother of the philologist Uno Lorenz Lindelöf....
. They jointly published this last version , known as the Phragmén–Lindelöf principle.
He leaves 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
Acta Mathematica is a journal publishing original research papers in all fields of mathematics. The journal was founded by Gösta Mittag-Leffler in 1882 and is published by Institut Mittag-Leffler, a research institute for mathematics belonging to the Royal Swedish Academy of Sciences...
. He is also famous for having pointed out (at 26) an unclear part of Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
's preprint on the three body problem. This lead Poincaré to discover a major mistake in his own work, paving the way to the important developments in chaos theory
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
.
Calculus aside, Phragmén was interested in the mathematics underlying insurance companies, and voting.