# Universal sampling discretization

@article{Dai2021UniversalSD, title={Universal sampling discretization}, author={Feng Dai and Vladimir N. Temlyakov}, journal={ArXiv}, year={2021}, volume={abs/2107.11476} }

Let XN be an N -dimensional subspace of L2 functions on a probability space (Ω, μ) spanned by a uniformly bounded Riesz basis ΦN . Given an integer 1 ≤ v ≤ N and an exponent 1 ≤ q ≤ 2, we obtain universal discretization for integral norms Lq(Ω, μ) of functions from the collection of all subspaces ofXN spanned by v elements of ΦN with the number m of required points satisfying m ≪ v(logN)2(log v)2. This last bound on m is much better than previously known bounds which are quadratic in v. Our… Expand

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