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Random Walk and the Heat Equation Gregory F. Lawler Department of Mathematics, University of Chicago, Chicago, IL 60637 E-mail address: [email protected]

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In mathematics, the question of whether the Fourier series of a periodic function converges to the given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics.

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Carleson’s theorem is a fundamental result in mathematical analysis establishing the pointwise almost everywhere convergence of Fourier series of L 2 functions, proved by Lennart Carleson ().