# Lennart A. E. Carleson

Wolf Prize Laureate in Mathematics 1992

**Lennart Carleson**

#### Affiliation at the time of the award:

**University of Uppsala****, Sweden**

**University of California****, USA**

#### Award citation:

**“for his fundamental contributions to Fourier analysis, complex analysis, quasiconformal mappings and dynamical systems”.**

#### Prize share:

**Lennart Carleson**

**John G. Thompson**

Lennart Carleson (born in 1928, Sweden) earned his Ph.D. from Uppsala University in 1950. He conducted post-doctoral research at Harvard University, where he engaged in discussions about Fourier series and their convergence with Antoni Zygmund and Raphaël Salem, who were present during 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, Carleson has also held the position of director at the Mittag-Leffler Institute in Djursholm, outside Stockholm, from 1968 to 1984. Additionally, he served as the president of the International Mathematical Union between 1978 and 1982.

Professor Lennart Carleson’s fundamental contributions to Fourier analysis, complex analysis, quasiconformal mappings, and dynamical systems have clearly established his position as one of the greatest analysts of the twentieth century. His 1952 Acta paper on sets of uniqueness for various classes of functions was the breakthrough paper in that area. The 1958 and 1962 papers on interpolation and the Corona problem not only solved the Corona Conjecture but introduced a host of new methods and concepts (e.g. Carleson measures, the Corona construction, and the relations to interpolation). These concepts are now central to modern Fourier analysis as well as complex analysis in both one and several variables.

Carleson’s celebrated solution of the Lusin conjecture in 1965 gave a dazzling display of his technical mastery and proved the now famous result that the Fourier series of an L² function on [0,1] converges almost everywhere. In 1972 Carleson proved that in dimension two Bochner-Riesz means of any order are LP bounded, 4/3 ≤ p ≤ 4. The methods introduced are again of fundamental importance to this area of Fourier analysis.

In 1974 he proved that a quasiconformal selfmap of R³ can be extended to be quasiconformal in R4. The earlier known cases of R and R² can be solved by elementary arguments; the deep methods he introduced have now been modified so as to work in arbitrary dimension.

In 1984 Carleson and Benedicks introduced a new method to study chaotic behavior of the map 1 → ax², and in 1988 they extended this method in a tour de force to prove that the Henon map (x ,y) → (1+y –ax, bx) exhibits “strange attractors” for a nonempty (even positive measure) set of parameter values. This historic paper has opened an entire area in dynamical systems.