Concept
Lennart Axel Edvard Carleson (born 18 March 1928) is a Swedish mathematician, known as a leader in the field of harmonic analysis. One of his most noted accomplishments is his proof of Lusin's conjecture. He was awarded the Abel Prize in 2006 for "his profound and seminal contributions to harmonic analysis and the theory of smooth dynamical systems." He was a student of Arne Beurling and received his Ph.D. from Uppsala University in 1950. He did his post-doctoral work at Harvard University where he met and discussed Fourier series and their convergence with Antoni Zygmund and Raphaël Salem who were there in 1950 and 1951. 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). He has supervised 29 PhD students. They include Svante Janson, Kurt Johansson, Warwick Tucker, Bengt Rosén, Per Sjölin, Hans Wallin and Ingemar Wik. His work has included the solution of some outstanding problems, using techniques from combinatorics and probability theory (especially stopping times). In the theory of Hardy spaces, Carleson's contributions include the corona theorem (1962), and establishing the almost everywhere convergence of Fourier series for square-integrable functions (now known as Carleson's theorem). It was a famous old problem by Joseph Fourier when he invented Fourier analysis in 1807 and formalised by Nikolai Luzin in 1913 as the Lusin's conjecture. Kolmogorov proved a famous negative result of the conjecture for L1 function in 1928 and stated that the conjecture must be false. It was so until 38 years later when Carleson gave his proof at the International Congress of Mathematicians at Moscow in 1966.
