Wavelet analysis: the scalable structure of information
Wavelet analysis: the scalable structure of information
Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration
Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration
On lower bounds for the L2-discrepancy
Journal of Complexity
Weighted discrepancy and numerical integration in function spaces
Journal of Complexity
Optimal cubature in Besov spaces with dominating mixed smoothness on the unit square
Journal of Complexity
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In a celebrated construction, Chen and Skriganov gave explicit examples of point sets achieving the best possible L"2-norm of the discrepancy function. We consider the discrepancy function of the Chen-Skriganov point sets in Besov spaces with dominating mixed smoothness and show that they also achieve the best possible rate in this setting. The proof uses a b-adic generalization of the Haar system and corresponding characterizations of the Besov space norm. Results for further function spaces and integration errors are concluded.