Record

EC - Certificates of election and candidature for Fellowship of the Royal Society
- 1993 - Certificates of Election 1993

RefNo	EC/1993/42
Level	Item
Title	Carleson, Lennart Axel Edvard: certificate of election to the Royal Society
Date	1990
Description	Certificate of Candidate for Election to Foreign Membership. Citation typed
Citation	Lennart Carleson is distinguished for his contributions to Mathematical Analysis. In this area he has solved some of the most important and difficult problems. Fourier discovered his series in the early years of the nineteenth century. They play a key role in periodic processes in Acoustics, Chrystallography [sic] and Signal Processing, to mention but a few. While every periodic Lebesgue integrable function f(x) can be expanded as a Fourier series f(x)~1/2 a-o + [sum from 1 to infinity] [a-n cos (nx) + b-n sin (nx)] Kolmogorov constructed in 1925 an example to show that such a series need not converge anywhere. Even the Fourier series of a continuous function can diverge at certain points. However Carleson proved in 1966 that if f(x)^2 is integrable, and in particular if f(x) is continuous, then the Fourier series of f(x) converges almost everywhere, i.e. outside a set of Lebesgue measure zero. In 1958 Carleson found necessary and sufficient conditions on a sequence z-n of points in the disk D:[z]<1, in order that every bounded complex sequence w-n be of the form w-n = f(z-n), where f is a bounded analytic function in D. His solution depended on a new concept, which is now called Carleson measure. These measures were also crucial for Carleson's solution in 1962 of another famous and difficult problem, the Corona Theorem. Carleson measure is a key concept in the theory of spaces on analytic functions and in particular in C. Fefferman's fundamental work on B.M.O. Strange attractors arise in analytical dynamics. Their properties have been studied for some time by Mathematicians and Physicists, but it is only recently that Carleson has proved that such objects actually exist. Carleson has written a book on exceptional sets. He has also worked on conformal and quasiconformal mapping and entropy and more recently and jointly with Peter Jones on coefficients of bounded and meromorphic univalent functions. In all these areas his contributions are seminal. Carleson's influence has been particularly powerful through his position as director of the Mittag-Leffler institute and editor of Acta Mathematica, one of the world's best mathematical journals. At the institute his ability to gather together leading mathematicians and to concentrate their energies on particular areas for six months or a year was particularly fruitful. Carleson has been a member of the Royal Swedish academy since 1957. He is a foreign member of the Finnish academy (1970) and an honorary member of the London Mathematical Society (1982). He was president of the International Mathematical Union from 1978 to 1982.
AccessStatus	Closed

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