Theorem

Carleson's Theorem

Analysis

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.

Facts

Statement

Carleson'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

Proof Year

1966 1

Classification

Statement Form

Existence Theorem 1

Sources

1. Carleson's theorem, Wikipedia

Lead section
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

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Carleson's Theorem