# Lennart Carleson

Lennart Carleson in 2006

Lennart Axel Edvard Carleson (born March 18, 1928 in Stockholm ) is a Swedish mathematician and winner of the Abel Prize .

## Life

Carleson received his doctorate in 1950 under Arne Beurling at Uppsala University ( On a class of meromorphic functions and its associated exceptional sets ). In 1950/1951 he was a post-doc at Harvard University (with Antoni Zygmund and Raphaël Salem ) and was a lecturer in Uppsala in 1951/52. In 1954 he became a professor at the Royal Technical University in Stockholm , but returned to Uppsala in 1955, where he retired in 1993. But he remained active in research. Among other things, he was visiting professor at the Massachusetts Institute of Technology (1957, 1974/75), at Stanford University (1965/66) and at the Institute for Advanced Study (1961/62).

In 1968, Carleson revitalized the Mittag-Leffler Institute , which he expanded as director from 1968 to 1984 into the center of mathematics in Scandinavia. Between 1978 and 1982 he was President of the International Mathematical Union . As president, among other things, he ensured the integration of China and the improvement of IT in the IMU, which was expressed, among other things, in the Nevanlinna Prize co-initiated by Carleson . 1956 to 1979 he was editor of Acta Mathematica.

He has been married since 1953 and has two children.

## plant

He worked in particular on function theory , Fourier analysis and dynamic systems . He became world famous in 1966, that by his proof Fourier series of function almost everywhere converges to the function. Nikolai Nikolajewitsch Lusin suspected this in 1913 (for continuous functions that belong to the square-integrable functions), but the proof resisted all attempts until 1966, one even suspected the existence of a counterexample, after Andrei Kolmogorow in 1923 a counterexample for the analogous conjecture with -functions found (and in 1926 even an example from this class of functions, the Fourier series of which diverged everywhere). Carleson also looked for a counterexample for a long time. Carleson's proof was simplified by Lars Hörmander in 1967 and extended by Richard Hunt in 1968 to -functions with finite p> 1. In 2000 Christoph Thiele and Michael T. Lacey gave a simpler proof of Carleson and Hunt's theorem. ${\ displaystyle L ^ {1}}$${\ displaystyle L ^ {p}}$

Carleson also proved the difficult Corona theorem in complex analysis in 1962, introducing Carleson measures . The American mathematician Thomas Wolff gave an alternative proof of the Corona theorem in 1979 .

In 1991 he and Michael Benedicks proved that the Hénon map , a much-studied dynamic system of chaos theory , introduced in 1976 by the French astronomer Michel Hénon , has a strange attractor .

The Carleson-Sjölin theorem of Fourier analysis is important in the Kakeya problem (generalizations of the Kakeya needle problem, which asks for the area of ​​minimal content in which a needle of unit length can rotate 180 °).

Carleson also promoted the extension problem of quasi-conformal mappings , for which Lars Ahlfors and Beurling already achieved partial results.

Carleson was co-editor of the collected works of his teacher Arne Beurling and commented on many of the works from Beurling's estate.

## Awards

Carleson is a member of the Russian, French, Danish, Swedish, Norwegian, Finnish and Hungarian Academies of Science as well as the National Academy of Sciences , the American Academy of Arts and Sciences and the Academia Europaea . He is honorary doctor in Helsinki, Paris, Stockholm. He is a fellow of the American Mathematical Society .

## Fonts

• Selected Problems on Exceptional Sets , Van Nostrand, 1967
• Matematik för vår tid (Mathematics for Our Time), Prisma 1968
• with TW Gamelin: Complex Dynamics , Springer, 1993