Lennart Carleson facts for kids
Quick facts for kids
Lennart Carleson
|
|
|---|---|
Lennart Carleson in May 2006.
|
|
| Born | 18 March 1928 |
| Nationality | Swedish |
| Alma mater | Uppsala University |
| Known for | Carleson–Jacobs theorem Carleson measure Carleson's theorem Corona theorem |
| Awards | Abel Prize (2006) Sylvester Medal (2003) Lomonosov Gold Medal (2002) Wolf Prize (1992) ForMemRS (1993) Leroy P. Steele Prize (1984) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Royal Institute of Technology Uppsala University University of California, Los Angeles |
| Doctoral advisor | Arne Beurling |
| Doctoral students | Svante Janson Kurt Johansson Warwick Tucker |
Lennart Axel Edvard Carleson (born March 18, 1928) is a Swedish mathematician. He is famous for his important work in a field called harmonic analysis, which studies waves and patterns. One of his biggest achievements was proving something called Lusin's conjecture. In 2006, he won the Abel Prize, which is like the Nobel Prize for mathematics. He received it for his "deep and important contributions" to harmonic analysis and the study of how systems change over time.
Life and Education
Lennart Carleson studied under a famous mathematician named Arne Beurling. He earned his Ph.D. (a high-level university degree) from Uppsala University in 1950. After that, he did more research at Harvard University in the United States. There, he met other mathematicians like Antoni Zygmund and Raphaël Salem. They discussed Fourier series, which are ways to break down complex waves into simpler ones.
Carleson is now a professor emeritus (a retired professor who keeps their title) at Uppsala University. He also taught at the Royal Institute of Technology in Stockholm and the University of California, Los Angeles. From 1968 to 1984, he was the director of the Mittag-Leffler Institute, a math research center near Stockholm. He also served as the president of the International Mathematical Union from 1978 to 1982. This is an organization that connects mathematicians worldwide.
In 1953, Carleson married Butte Jonsson. They had two children, Caspar (born 1955) and Beatrice (born 1958). He has guided 29 students through their Ph.D. studies. Some of his notable students include Svante Janson, Kurt Johansson, and Warwick Tucker.
His Mathematical Work
Lennart Carleson is known for solving some very difficult mathematical problems. He used special techniques from combinatorics (the study of counting and arrangements) and probability theory (the study of chance).
In a field called Hardy spaces, Carleson made several key discoveries. These include the corona theorem in 1962. He also proved that Fourier series for certain types of functions (called square-integrable functions) always come together, or "converge," almost everywhere. This is now known as Carleson's theorem.
This problem was first thought about by Joseph Fourier in 1807. It was later made into a clear question by Nikolai Luzin in 1913, known as Lusin's conjecture. Another mathematician, Kolmogorov, had shown in 1928 that the conjecture was false for some functions. He even thought it must be false in general. But 38 years later, in 1966, Carleson proved it was true for square-integrable functions at a big math meeting in Moscow. His proofs were very complex at first. However, as mathematicians developed new tools, his amazing ideas became easier to understand and use.
Carleson is also known for his work on Carleson measures. His ideas and methods have been very important for many areas of mathematics. For example, a theorem he developed with Per Sjölin is now standard in the study of the Kakeya problem. In 1974, he also solved a problem related to quasiconformal mappings and made important discoveries about Bochner–Riesz means in two dimensions.
In the study of dynamical systems (how systems change over time), Carleson worked on complex dynamics. In 1991, he and Michael Benedicks proved that "strange attractors" exist in something called the Hénon map. This discovery opened up a new area of study in dynamical systems.
Besides writing many important research papers, Carleson has also written two books. One is an influential book on potential theory called Selected Problems on Exceptional Sets (1967). The other, Complex Dynamics (1993), is about how analytic functions repeat themselves, and he wrote it with T. W. Gamelin. He also helped collect and publish the unreleased works of his mentor, Arne Beurling, in 1989.
Awards and Recognition
Lennart Carleson has received many prestigious awards for his mathematical work:
- Wolf Prize in Mathematics in 1992
- Lomonosov Gold Medal in 2002
- Sylvester Medal in 2003
- Abel Prize in 2006
He is a member of many important scientific groups, including the Norwegian Academy of Science and Letters. In 2012, he became a fellow of the American Mathematical Society. He is also a Foreign Fellow of the Royal Society (since 1993) and an Honorary member of the London Mathematical Society (since 1981). Other memberships include the American Academy of Arts and Sciences, French Academy of Sciences, and the Royal Swedish Academy of Sciences. He has also received honorary doctorates from many universities, such as Helsinki, Paris, and KTH Royal Institute of Technology in Stockholm.
See also
In Spanish: Lennart Carleson para niños
