Torsten Carleman
Encyclopedia
Torsten Carleman born Tage Gills Torsten Carleman, was a Swedish
mathematician
.
Carleman obtained important results in various branches of analysis
, in particular, the theory of quasi-analytic functions (where he proved the Denjoy–Carleman theorem, which gives a necessary and sufficient condition for quasi-analyticity), complex analysis
(where he established the Carleman formula), harmonic analysis
, approximation theory
, and the moment problem (where he found a sufficient condition
for determinacy). He is also remembered for his work on singular integral equation
s, and on the kinetic theory
of gases (in particular, Boltzmann's equation).
He was elected a member of the Royal Swedish Academy of Sciences
in 1926. From 1927, he was director of the Mittag-Leffler Institute
.
Carleman's abuse of alcohol was described by Norbert Wiener
and by William Feller
.
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
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Carleman obtained important results in various branches of analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, in particular, the theory of quasi-analytic functions (where he proved the Denjoy–Carleman theorem, which gives a necessary and sufficient condition for quasi-analyticity), 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,...
(where he established the Carleman formula), harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...
, approximation theory
Approximation theory
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby...
, and the moment problem (where he found a sufficient condition
Carleman's condition
In mathematics, Carleman's condition is a sufficient condition for the determinacy of the moment problem.-Hamburger moment problem:For the Hamburger moment problem, the theorem, proved by Torsten Carleman, states the following:...
for determinacy). He is also remembered for his work on singular integral equation
Integral equation
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way...
s, and on the kinetic theory
Kinetic theory
The kinetic theory of gases describes a gas as a large number of small particles , all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container...
of gases (in particular, Boltzmann's equation).
He was elected a member of the Royal Swedish Academy of Sciences
Royal Swedish Academy of Sciences
The Royal Swedish Academy of Sciences or Kungliga Vetenskapsakademien is one of the Royal Academies of Sweden. The Academy is an independent, non-governmental scientific organization which acts to promote the sciences, primarily the natural sciences and mathematics.The Academy was founded on 2...
in 1926. From 1927, he was director of the Mittag-Leffler Institute
Mittag-Leffler Institute
The Mittag-Leffler Institute is a mathematical research institute located in Djursholm, a suburb of Stockholm. It invites scholars to participate in year-long or half-year programs in specialized mathematical subjects...
.
Carleman's abuse of alcohol was described by Norbert Wiener
Norbert Wiener
Norbert Wiener was an American mathematician.A famous child prodigy, Wiener later became an early researcher in stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.Wiener is regarded as the originator of cybernetics, a...
and by William Feller
William Feller
William Feller born Vilibald Srećko Feller , was a Croatian-American mathematician specializing in probability theory.-Early life and education:...
.