Lower Bounds for the Directional Discrepancy with Respect to an Interval of Rotations

Dmitriy Bilyk; Michelle Mastrianni

doi:10.1007/s00041-023-10005-7

Lower Bounds for the Directional Discrepancy with Respect to an Interval of Rotations

Dmitriy Bilyk, Michelle Mastrianni

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the lower bound for the optimal directional discrepancy with respect to the class of rectangles in R² rotated in a restricted interval of directions [- θ, θ] with θ<π4 is of the order at least N^{1 / 5} with a constant depending on θ .

Original language	English (US)
Article number	25
Journal	Journal of Fourier Analysis and Applications
Volume	29
Issue number	3
DOIs	https://doi.org/10.1007/s00041-023-10005-7
State	Published - Jun 2023

Bibliographical note

Funding Information:
D. Bilyk and M. Mastrianni have been supported by the National Science Foundation (Grant DMS 2054606).

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Average decay of the Fourier transform
Discrepancy
Uniform distribution

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10.1007/s00041-023-10005-7

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Lower Bounds for the Directional Discrepancy with Respect to an Interval of Rotations

Abstract

Bibliographical note

Keywords

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