Theory of Computing Systems

, Volume 63, Issue 3, pp 567–586 | Cite as

Algorithmic Randomness and Fourier Analysis

  • Johanna N. Y. Franklin
  • Timothy H. McNichollEmail author
  • Jason Rute


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 fLp[−π, π] given natural computability conditions on f and p.


Computability Fourier analysis Complex analysis Algorithmic randomness Computable analysis 



We are grateful for the helpful comments made by the anonymous referees.

The first author was supported in part by Simons Foundation grant # 420806. Research of the second author was supported in part by Simons Foundation grant #317870.


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Authors and Affiliations

  1. 1.Department of MathematicsHofstra UniversityHempsteadUSA
  2. 2.Department of MathematicsIowa State UniversityAmesUSA
  3. 3.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

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