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The Marcinkiewicz-Type Discretization Theorems

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Abstract

This paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. This problem is very important in applications, but there is no systematic study of it. We present here a new technique, which works well for discretization of the integral norm. It is a combination of probabilistic technique, based on chaining, and results on the entropy numbers in the uniform norm.

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Acknowledgements

The work was supported by the Russian Federation Government Grant No. 14.W03.31.0031.

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Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, 1523 Greene Str., Columbia, SC, 29208, USA

    V. N. Temlyakov

  2. Steklov Institute of Mathematics, Moscow, Russia

    V. N. Temlyakov

  3. Lomonosov Moscow State University, Moscow, Russia

    V. N. Temlyakov

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  1. V. N. Temlyakov
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Correspondence to V. N. Temlyakov.

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Communicated by Ronald A. DeVore.

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Temlyakov, V.N. The Marcinkiewicz-Type Discretization Theorems. Constr Approx 48, 337–369 (2018). https://doi.org/10.1007/s00365-018-9446-2

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  • DOI: https://doi.org/10.1007/s00365-018-9446-2

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