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.

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.

Copyright Owner

Springer Science+Business Media, LLC, part of Springer Nature

Language

en

File Format

application/pdf

Published Version

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