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Sampling Discretization of Integral Norms of the Hyperbolic Cross Polynomials

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Abstract

The paper is devoted to discretization of integral norms of functions from a given finite-dimensional subspace. We use recent general results on sampling discretization to derive a new Marcinkiewicz type discretization theorem for the multivariate trigonometric polynomials with frequencies from the hyperbolic crosses. It is shown that recently developed techniques allow us to improve the known results in this direction.

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Funding

The work was supported by the Government of the Russian Federation, grant no. 14.W03.31.0031.

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Authors and Affiliations

  1. University of South Carolina, Columbia, SC, 29208, USA

    V. N. Temlyakov

  2. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    V. N. Temlyakov

  3. Lomonosov Moscow State University, Moscow, 119991, Russia

    V. N. Temlyakov

  4. Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia

    V. N. Temlyakov

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

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 312, pp. 282–293 https://doi.org/10.4213/tm4133.

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Temlyakov, V.N. Sampling Discretization of Integral Norms of the Hyperbolic Cross Polynomials. Proc. Steklov Inst. Math. 312, 270–281 (2021). https://doi.org/10.1134/S0081543821010181

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  • DOI: https://doi.org/10.1134/S0081543821010181

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