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Entropy numbers and Marcinkiewicz-type discretization theorem

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arxiv 2001.10636 v1 pith:DME6OKBU submitted 2020-01-28 math.CA

F. Dai , A. Prymak , A. Shadrin , V. Temlyakov , S. Tikhonov This is my paper · ORCID
classification math.CA
keywords entropynumbersdimensionaldiscretizationfinitefunctionsgivenintegral
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This paper studies the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspace. Upper bounds of these entropy numbers in the uniform norm are obtained and applied to establish a Marcinkiewicz type discretization theorem for integral norms of functions from a given finite dimensional subspace.

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    Sparse approximation of kernels with adaptive, kernel-dependent dictionaries controls sampling-recovery errors for families of integral-operator function classes.

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