Lennart Carleson
Encyclopedia
Lennart Axel Edvard Carleson (born 18 March 1928) is a Swedish
mathematician
, known as a leader in the field of harmonic analysis
.
and received his Ph.D.
from Uppsala University
in 1950. He is a professor emeritus at Uppsala University, the Royal Institute of Technology
in Stockholm
, and the University of California, Los Angeles
, and has served as director of the Mittag-Leffler Institute
in Djursholm
outside Stockholm 1968–1984. Between 1978 and 1982 he served as president of the International Mathematical Union
.
Carleson married Butte Jonsson in 1953, and they had two children: Caspar (born 1955) and Beatrice (born 1958).
and probability theory
(especially stopping times). In the theory of Hardy space
s, Carleson's contributions include the corona theorem
(1962) and establishing the almost everywhere
convergence of Fourier series
for square-integrable function
s (now known as Carleson's theorem
). He is also known for the theory of Carleson measure
s.
In the theory of dynamical system
s, Carleson has worked in complex dynamics
.
In addition to publishing some landmark papers, Carleson has also published two books: First, an influential book on potential theory
, "Selected Problems on Exceptional Sets" (Van Nostrand, 1967), and second a book on the iteration of analytic function
s, Complex Dynamics (Springer, 1993, in collaboration with T. W. Gamelin).
in 1992, the Lomonosov Gold Medal
in 2002, the Sylvester Medal
in 2003, and the Abel Prize
in 2006 for his profound and seminal contributions to harmonic analysis and the theory of smooth dynamic systems.
He is a member of the Norwegian Academy of Science and Letters
.
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....
, known as a leader in the field of 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...
.
Life
He was a student of Arne BeurlingArne Beurling
Arne Carl-August Beurling was a Swedish mathematician and professor of mathematics at Uppsala University and later at the Institute for Advanced Study in Princeton, New Jersey....
and received his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
from Uppsala University
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...
in 1950. He is a professor emeritus at Uppsala University, the Royal Institute of Technology
Royal Institute of Technology
The Royal Institute of Technology is a university in Stockholm, Sweden. KTH was founded in 1827 as Sweden's first polytechnic and is one of Scandinavia's largest institutions of higher education in technology. KTH accounts for one-third of Sweden’s technical research and engineering education...
in Stockholm
Stockholm
Stockholm is the capital and the largest city of Sweden and constitutes the most populated urban area in Scandinavia. Stockholm is the most populous city in Sweden, with a population of 851,155 in the municipality , 1.37 million in the urban area , and around 2.1 million in the metropolitan area...
, and the University of California, Los Angeles
University of California, Los Angeles
The University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...
, and has served as 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...
in Djursholm
Djursholm
Djursholm is one of four suburban districts in, and the seat of Danderyd Municipality, Stockholm County, Sweden. Djursholm is included in the multi-municipal Stockholm urban area.-History:...
outside Stockholm 1968–1984. Between 1978 and 1982 he served as president of the International Mathematical Union
International Mathematical Union
The International Mathematical Union is an international non-governmental organisation devoted to international cooperation in the field of mathematics across the world. It is a member of the International Council for Science and supports the International Congress of Mathematicians...
.
Carleson married Butte Jonsson in 1953, and they had two children: Caspar (born 1955) and Beatrice (born 1958).
Work
His work has included the solution of some outstanding problems, using techniques from combinatoricsCombinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
and probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
(especially stopping times). In the theory of Hardy space
Hardy space
In complex analysis, the Hardy spaces Hp are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz , who named them after G. H. Hardy, because of the paper...
s, Carleson's contributions include the corona theorem
Corona theorem
In mathematics, the corona theorem is a result about the spectrum of the bounded holomorphic functions on the open unit disc, conjectured by and proved by ....
(1962) and establishing the almost everywhere
Almost everywhere
In measure theory , a property holds almost everywhere if the set of elements for which the property does not hold is a null set, that is, a set of measure zero . In cases where the measure is not complete, it is sufficient that the set is contained within a set of measure zero...
convergence of Fourier series
Convergence of Fourier series
In mathematics, the question of whether the Fourier series of a periodic function converges to the given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics...
for square-integrable function
Square-integrable function
In mathematics, a quadratically integrable function, also called a square-integrable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite...
s (now known as Carleson's theorem
Carleson's theorem
Carleson's theorem is a fundamental result in mathematical analysis establishing the pointwise almost everywhere convergence of Fourier series of L2 functions, proved by...
). He is also known for the theory of Carleson measure
Carleson measure
In mathematics, a Carleson measure is a type of measure on subsets of n-dimensional Euclidean space Rn. Roughly speaking, a Carleson measure on a domain Ω is a measure that does not vanish at the boundary of Ω when compared to the surface measure on the boundary of Ω.Carleson measures have many...
s.
In the theory of dynamical system
Dynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...
s, Carleson has worked in complex dynamics
Complex dynamics
Complex dynamics is the study of dynamical systems defined by iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions.-Techniques:*General** Montel's theorem...
.
In addition to publishing some landmark papers, Carleson has also published two books: First, an influential book on potential theory
Potential theory
In mathematics and mathematical physics, potential theory may be defined as the study of harmonic functions.- Definition and comments :The term "potential theory" was coined in 19th-century physics, when it was realized that the fundamental forces of nature could be modeled using potentials which...
, "Selected Problems on Exceptional Sets" (Van Nostrand, 1967), and second a book on the iteration of analytic function
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others...
s, Complex Dynamics (Springer, 1993, in collaboration with T. W. Gamelin).
Awards
He was awarded the Wolf Prize in MathematicsWolf Prize in Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts...
in 1992, the Lomonosov Gold Medal
Lomonosov Gold Medal
The Lomonosov Gold Medal, named after Russian scientist and polymath Mikhail Lomonosov, is awarded each year since 1959 for outstanding achievements in the natural sciences and the humanities by the USSR Academy of Sciences and later the Russian Academy of Sciences . Two medals are awarded...
in 2002, the Sylvester Medal
Sylvester Medal
The Sylvester Medal is a bronze medal awarded by the Royal Society for the encouragement of mathematical research, and accompanied by a £1,000 prize...
in 2003, and the Abel Prize
Abel Prize
The Abel Prize is an international prize presented annually by the King of Norway to one or more outstanding mathematicians. The prize is named after Norwegian mathematician Niels Henrik Abel . It has often been described as the "mathematician's Nobel prize" and is among the most prestigious...
in 2006 for his profound and seminal contributions to harmonic analysis and the theory of smooth dynamic systems.
He is a member of the Norwegian Academy of Science and Letters
Norwegian Academy of Science and Letters
The Norwegian Academy of Science and Letters is a learned society based in Oslo, Norway.-History:The University of Oslo was established in 1811. The idea of a learned society in Christiania surfaced for the first time in 1841. The city of Throndhjem had no university, but had a learned...
.
External links
- Abel Prize press release and biography (PDF file)