Weighted L_2 B Discrepancy and Approximation of Integrals over Reproducing Kernel Hilbert Spaces
نویسنده
چکیده
We extend the notion of L2 B discrepancy provided in [E. Novak, H. Woźniakowski, L2 discrepancy and multivariate integration, in: Analytic number theory. Essays in honour of Klaus Roth. W. W. L. Chen, W. T. Gowers, H. Halberstam, W. M. Schmidt, and R. C. Vaughan (Eds.), Cambridge University Press, Cambridge, 2009, 359 – 388] to the weighted L2 B discrepancy. This newly defined notion allows to consider weights, but also volume measures different from the Lebesgue measure and classes of test sets different from measurable subsets of some Euclidean space. We relate the weighted L2 B discrepancy to numerical integration defined over weighted reproducing kernel Hilbert spaces and settle in this way an open problem posed by Novak and Woźniakowski.
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