# 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…

## One Citation

On universal sampling representation

- Computer Science, MathematicsArXiv
- 2022

This work replaces the normalized Lebesgue measure by a discrete measure in such a way, which preserves the convolution properties and provides sampling discretization of integral norms, that in the two-variate case the Fibonacci point sets provide an ideal solution.

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