# Algorithmic Randomness and Fourier Analysis

@article{Franklin2018AlgorithmicRA, title={Algorithmic Randomness and Fourier Analysis}, author={Johanna N. Y. Franklin and Timothy H. McNicholl and Jason Rute}, journal={Theory of Computing Systems}, year={2018}, volume={63}, pages={567-586} }

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.

2

Twitter Mentions

#### Topics from this paper.

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 70 REFERENCES

## Schnorr randomness and the Lebesgue differentiation theorem

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Randomness and Non-ergodic Systems

VIEW 2 EXCERPTS

## Topics in algorithmic randomness and computable analysis

VIEW 7 EXCERPTS

## Algorithmic Aspects of Lipschitz Functions

VIEW 3 EXCERPTS

## L1-Computability, Layerwise Computability and Solovay Reducibility

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Computability of the ergodic decomposition

VIEW 1 EXCERPT

## Randomness and Differentiability

VIEW 2 EXCERPTS