Corpus ID: 237571677

Sampling discretization of integral norms and its application

@article{Dai2021SamplingDO,
  title={Sampling discretization of integral norms and its application},
  author={Feng Dai and Vladimir N. Temlyakov},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.09030}
}
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 two standard kinds of assumptions – conditions on the entropy numbers and conditions in terms of the Nikol’skii-type inequalities. We prove some upper bounds on the number of sample points sufficient for good discretization and show that these upper bounds are sharp in a certain sense. Then we apply our… Expand

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