Algorithmic randomness and Fourier analysis

2016/03/06 by Johanna Franklin, Franklin, Johanna, Timothy McNicholl +3
Mathematics · #03D32 (Primary) 03D78 #42A20 (Secondary) #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03D32 #msc:03D78 #msc:42A20

paper · pdf · doi:10.48550/arxiv.1603.01778

arxiv created 2016/03/06 · arxiv updated 2016/03/16

Abstract

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

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