Carleson's Theorem states that the Fourier series of a square-integrable function converges to the function pointwise almost everywhere, resolving a convergence question that had been open since the nineteenth century. Named for Lennart Carleson, who proved it in 1966, it settled the pointwise convergence problem for a very broad class of functions and was later extended by Richard Hunt to a wider range of function spaces.
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StatementCarleson's theorem is a fundamental result in mathematical analysis establishing the pointwise almost everywhere convergence of Fourier series of L2 functions, proved by Lennart Carleson. 1 Classification
Statement Form Carleson's Theorem
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Source Carleson's theorem, Wikipedia
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Source Wikipedia: Lennart Carleson
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Source Carleson's theorem, Wikipedia
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Carleson's theorem is a fundamental result in mathematical analysis establishing the (Lebesgue) pointwise almost everywhere convergence of Fourier series of L2 functions, proved by Lennart Carleson.
References section
Carleson, Lennart (1966). On convergence and growth of partial sums of Fourier series
In Branch: Analysis, Lead sentence
Carleson's theorem is a fundamental result in mathematical analysis establishing the (Lebesgue) pointwise almost everywhere conver
Proved By: Lennart Carleson, Lead sentence, attribution
proved by Lennart Carleson
View the SourceWikipedia: Lennart Carleson
Principal Result Of: Lennart Carleson, Article textQuote, Principal Result Of: Lennart Carleson, Article text
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).
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