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

We show that the lower bound for the optimal directional discrepancy with respect to the class of rectangles in R 2 rotated in a restricted interval of directions [ - θ , θ ] with θ < π 4 is of the order at least N 1 / 5 with a constant depending on θ .

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2023-06, Vol.29 (3), Article 25
Main Authors: Bilyk, Dmitriy, Mastrianni, Michelle
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Approximations and Expansions
Fourier Analysis
Lower bounds
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Signal,Image and Speech Processing
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Description
Summary:We show that the lower bound for the optimal directional discrepancy with respect to the class of rectangles in R 2 rotated in a restricted interval of directions [ - θ , θ ] with θ < π 4 is of the order at least N 1 / 5 with a constant depending on θ .
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-023-10005-7