Campus Units
Mathematics
Document Type
Article
Publication Version
Accepted Manuscript
Publication Date
4-15-2019
Journal or Book Title
Theory of Computing Systems
Volume
63
First Page
567
Last Page
586
DOI
10.1007/s00224-018-9888-8
Abstract
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.
Copyright Owner
Springer Science+Business Media, LLC, part of Springer Nature
Copyright Date
2018
Language
en
File Format
application/pdf
Recommended Citation
Franklin, Johanna N. Y.; McNicholl, Timothy H.; and Rute, Jason, "Algorithmic Randomness and Fourier Analysis" (2019). Mathematics Publications. 261.
https://lib.dr.iastate.edu/math_pubs/261
Comments
This is a manuscript of an article published as Franklin, J.N.Y., McNicholl, T.H. & Rute, J. Algorithmic Randomness and Fourier Analysis. Theory Comput Syst 63, 567–586 (2019). doi: 10.1007/s00224-018-9888-8. Posted with permssion.