Algorithmic randomness and Fourier analysis
| Autor: | Jason Rute, Johanna N. Y. Franklin, Timothy H. McNicholl |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Computability 010102 general mathematics Algorithmic randomness Function (mathematics) Mathematics - Logic 01 natural sciences Computable analysis Theoretical Computer Science 03 medical and health sciences symbols.namesake 0302 clinical medicine Computational Theory and Mathematics Fourier analysis Theory of computation symbols FOS: Mathematics Almost everywhere 030212 general & internal medicine 0101 mathematics 03D32 (Primary) 03D78 42A20 (Secondary) Logic (math.LO) Fourier series Mathematics |
| DOI: | 10.48550/arxiv.1603.01778 |
| Popis: | Suppose $1 < p < \infty$. Carleson's Theorem states that the Fourier series of any function in $L^p[-��, ��]$ converges almost everywhere. We show that the Schnorr random points are precisely those that satisfy this theorem for every $f \in L^p[-��, ��]$ given natural computability conditions on $f$ and $p$. |
| Databáze: | OpenAIRE |
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