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 Roth’s orthogonal function method among a large class of test functions. We use methods of combinatorics, probability, and...
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| Veröffentlicht in: | Mathematika 2013-07, Vol.59 (2), p.365-379 |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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 Roth’s orthogonal function method among a large class of test functions. We use methods of combinatorics, probability, and complex and harmonic analysis. |
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| ISSN: | 0025-5793 2041-7942 |
| DOI: | 10.1112/S0025579312001180 |