Proving a 43-year-old conjecture at the 1966 International Congress of Mathematicians in Moscow established the global reputation of Lennart Carleson. His solution confirmed that the Fourier series of any square-integrable function converges almost everywhere, addressing a challenge originally posed by Joseph Fourier in 1807 and subsequently formalised by Nikolai Luzin in 1913.
Academic Foundation
Born in 1928 in Stockholm, Carleson pursued his advanced studies at Uppsala University between 1945 and 1950 under the guidance of Arne Beurling. He expanded his mathematical research at Harvard University during 1950 and 1951, where he engaged with specialists such as Antoni Zygmund and Raphaël Salem. This period facilitated his early focus on Fourier series and harmonic analysis.
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Carleson held academic appointments at Stockholm University from 1954 to 1955, and Uppsala University between 1951 and 1954, as well as 1955 to 1993. Beyond his domestic duties, he served as a professor at the University of California, Los Angeles, in 1991. Between 1968 and 1984, he directed the Mittag-Leffler Institute, playing a central role in the organisation of European mathematical research.
Analytical Innovations
His work extends into complex dynamics and the theory of Hardy spaces, notably the 1962 corona theorem. He developed the theory of Carleson measures and, in 1974, resolved the extension problem for quasiconformal mappings. In 1991, he collaborated with Michael Benedicks to demonstrate the existence of strange attractors within the Hénon map, introducing significant methods to the study of dynamical systems.
Recognition and Membership
The international community recognised his contributions through the Wolf Prize in 1992, the Lomonosov Gold Medal in 2002, the Sylvester Medal in 2003, and the Abel Prize in 2006. He holds memberships in numerous prestigious organisations, including the Royal Swedish Academy of Sciences, the Russian Academy of Sciences, the French Academy of Sciences, and the National Academy of Sciences.
Fast facts
- Born: 1928, Stockholm
- Primary Field: Harmonic Analysis
- Doctoral Alma Mater: Uppsala University
- Abel Prize: 2006
- Wolf Prize in Mathematics: 1992
- Notable Achievement: Proof of Lusin's conjecture
- Foreign Member of the Royal Society: 1993
Questions readers ask
What is Carleson's theorem?
It is a mathematical proof establishing that the Fourier series of any square-integrable function converges almost everywhere, solving a problem first proposed in 1807.
Where did Lennart Carleson hold professorships?
He held positions at Uppsala University, Stockholm University, and the University of California, Los Angeles.
Achievements
- Leroy P. Steele Prize — 1984
- Wolf Prize in Mathematics — 1992
- Lomonosov Gold Medal — 2002
- Sylvester Medal — 2003
- Abel Prize — 2006
- Notable work: Carleson's theorem
- Notable work: Carleson–Jacobs theorem
- Notable work: Carleson measure
- Held posts at Uppsala University, Stockholm University and Uppsala University
- Fields: mathematics, Fourier series and harmonic analysis
