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arXiv · 1603.01778

Algorithmic randomness and Fourier analysis

Johanna Franklin·Timothy McNicholl·Jason Rute
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Abstract

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

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Johanna Franklin, Timothy McNicholl, Jason Rute. 2016-03-06. Algorithmic randomness and Fourier analysis. https://arxiv.org/abs/1603.01778

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