This article is cited in 6 papers

One-sided discretization inequalities and sampling recovery

I. V. Limonova^abc, Yu. V. Malykhin^ab, V. N. Temlyakov<sup>abcd

a</sup> Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
^b Lomonosov Moscow State University
^c Moscow Center for Fundamental and Applied Mathematics
^d University of South Carolina, Columbia, SC, USA

Abstract: Recently, in a number of papers it was understood that results on sampling discretization and universal sampling discretization can successfully be used in the problem of sampling recovery. Moreover, it turns out that it is sufficient to only have a one-sided discretization inequality for some of these applications. This motivated us to write the present paper as a survey, which includes new results, with the focus on the one-sided discretization inequalities and their applications to sampling recovery. In this sense the paper complements the two existing survey papers on sampling discretization (Russian Math. Surveys, 74:4 (2019), 579–630 and J. Complexity, 71 (2022), 101653, 55 pp.).
Bibliography: 50 titles.

Keywords: sampling discretization, Nikol'skii's inequality, recovery.

UDC: 517.5

MSC: 65J05

Received: 10.04.2024

DOI: 10.4213/rm10175

 English version: Russian Mathematical Surveys, 2024, 79:3, 515–545

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