# Sampling discretization of the uniform norm

@inproceedings{Kashin2021SamplingDO, title={Sampling discretization of the uniform norm}, author={Boris Kashin and Sergei Konyagin and Vladimir N. Temlyakov}, year={2021} }

Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of trigonometric polynomials with frequencies from an arbitrary finite set with fixed cardinality. We give two different proofs of the fact that for any N -dimensional subspace of the space of continuous functions it is sufficient to use eCN sample points for an accurate upper bound for the uniform norm. Previous known results show…

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