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arXiv · 2208.09762

Some improved bounds in sampling discretization of integral norms

F. Dai·E. Kosov·V. Temlyakov
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Abstract

The paper addresses a problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under a standard assumption formulated in terms of the Nikol'skii-type inequality. {In particular, we obtain} some upper bounds on the number of sample points sufficient for good discretization of the integral $L_p$ norms, $1\le p<2$, of functions from finite-dimensional subspaces of continuous functions. Our new results improve upon the known results in this direction. We use a new technique based on deep results of Talagrand from functional analysis.

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BibTeXRIS

F. Dai, E. Kosov, V. Temlyakov. 2022-08-20. Some improved bounds in sampling discretization of integral norms. https://arxiv.org/abs/2208.09762

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