Lennart Carleson

Lennart Carleson ( born March 18, 1928 in Stockholm ) is a Swedish mathematician and Abel prize winners.

Life

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

Carleson busy 1968, the Mittag-Leffler Institute new, that he developed as a director from 1968 to 1984 to the center of mathematics in Scandinavia. Between 1978 and 1982 he was president of the International Mathematical Union. He made as president, among other things for the involvement of China and the betterment of computer science in the IMU, which was reflected inter alia in the co-initiated by Carleson Nevanlinna Prize. 1956 to 1979 he was editor of Acta Mathematica.

He has been married since 1953 and has two children.

Work

He worked in particular on complex analysis, Fourier analysis, and dynamical systems. World famous he was in 1966 by his proof that the Fourier series of an L ² function almost everywhere converges to the function. Had suspected this 1913 Nikolai Nikolaevich Luzin ( for continuous functions belonging to the square integrable functions ), the proof resistant but until 1966 all the experiments, one even suspected the existence of a counter-example after Andrei Kolmogorov in 1923 a counter-example for the analogous conjecture for functions found ( and 1926 even an example of this class of functions whose Fourier series diverge everywhere ). Also Carleson, it was first time a counterexample. The proof of Carleson has been simplified by Lars Hörmander 1967 and 1968 expanded by Richard Hunt on functions with finite p> 1. Christoph Thiele and Michael T. Lacey gave 2000 a simpler proof of the theorem of Carleson and Hunt.

Carleson proved in 1962 the difficult corona theorem in complex analysis, in which he introduced Carleson measures. An alternative proof of the corona theorem was 1979, the American mathematician Thomas Wolff.

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

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

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

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

Awards

Carleson is a member of the Russian, French, Danish, Swedish, Norwegian, Finnish and Hungarian Academies of Sciences and the American Academy of Arts and Sciences. He holds an honorary doctorate in Helsinki, Paris, Stockholm. He is a Fellow of the American Mathematical Society.

Writings

  • Selected problem on Exceptional Sets, Van Nostrand, 1967
  • Matematik för vår tid ( Mathematics for our time), Prism 1968
  • With TW Gamelin: Complex Dynamics, Springer, 1993
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