Approximation properties of certain operator-induced norms on Hilbert spaces
نویسندگان
چکیده
We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2. The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in a reproducing kernel Hilbert space (RKHS). Our results have implications to the analysis of M-estimators in models based on finite-dimensional linear approximation of functions, and also to some related packing problems. c ⃝ 2011 Elsevier Inc. All rights reserved.
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عنوان ژورنال:
- Journal of Approximation Theory
دوره 164 شماره
صفحات -
تاریخ انتشار 2012