Algorithmic Randomness and Fourier Analysis
2019
Suppose 1 < p < ∞. Carleson’s Theorem states that the Fourier series of any function in Lp[−π, π] converges almost everywhere. We show that the Schnorr random points are precisely those that satisfy this theorem for every f ∈ Lp[−π, π] given natural computability conditions on f and p.
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