# Sampling Discretization of Integral Norms of the Hyperbolic Cross Polynomials

@article{Temlyakov2020SamplingDO, title={Sampling Discretization of Integral Norms of the Hyperbolic Cross Polynomials}, author={Vladimir N. Temlyakov}, journal={Proceedings of the Steklov Institute of Mathematics}, year={2020}, volume={312}, pages={270-281} }

Abstract The paper is devoted to discretization of integral norms of functions from a given finite-dimensional subspace. We use recent general results on sampling discretization to derive a new Marcinkiewicz type discretization theorem for the multivariate trigonometric polynomials with frequencies from the hyperbolic crosses. It is shown that recently developed techniques allow us to improve the known results in this direction.

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## 5 Citations

Sampling discretization of integral norms and its application

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This paper proves sampling discretization results under two standard kinds of assumptions – conditions on the entropy numbers and conditions in terms of the Nikol’skii-type inequalities, and applies these results to subspaces with special structure.

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This survey addresses sampling discretization and its connections with other areas of mathematics. We present here known results on sampling discretization of both integral norms and the uniform norm…

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The focus will be on the behavior of the best m-term trigonometric approximation as well as the decay of Kolmogorov and entropy numbers in the uniform norm, which have direct implications for the problem of sampling recovery in L2.

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