$$L^{p}$$ L p Norms of the Lattice Point Discrepancy
نویسندگان
چکیده
منابع مشابه
Lp discrepancy of generalized two-dimensional Hammersley point sets
We determine the Lp discrepancy of the two-dimensional Hammersley point set in base b. These formulas show that the Lp discrepancy of the Hammersley point set is not of best possible order with respect to the general (best possible) lower bound on Lp discrepancies due to Roth and Schmidt. To overcome this disadvantage we introduce permutations in the construction of the Hammersley point set and...
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15 صفحه اولBounds for the Average Lp-Extreme and the L∞-Extreme Discrepancy
The extreme or unanchored discrepancy is the geometric discrepancy of point sets in the d-dimensional unit cube with respect to the set system of axis-parallel boxes. For 2 ≤ p < ∞ we provide upper bounds for the average Lp-extreme discrepancy. With these bounds we are able to derive upper bounds for the inverse of the L∞-extreme discrepancy with optimal dependence on the dimension d and explic...
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2019
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-019-09665-1