Lower Bounds for \(L_1\) Discrepancy

We find the best asymptotic lower bounds for the coefficient of the leading term of the \(L_1\) norm of the two-dimensional (axis-parallel) discrepancy that can be obtained by K.Roth's orthogonal function method among a large class of test functions. We use methods of combinatorics, probability...

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Bibliographic Details
Published in:arXiv.org 2012-11
Main Author: Vagharshakyan, Armen
Format: Article
Language:English
Subjects:
Combinatorial analysis
Fourier analysis
Harmonic analysis
Lower bounds
Orthogonal functions
Probabilistic methods
Queuing theory
Test procedures
Online Access:Get full text
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Summary:We find the best asymptotic lower bounds for the coefficient of the leading term of the \(L_1\) norm of the two-dimensional (axis-parallel) discrepancy that can be obtained by K.Roth's orthogonal function method among a large class of test functions. We use methods of combinatorics, probability, complex and harmonic analysis.
ISSN:2331-8422
DOI:10.48550/arxiv.1209.2398