Sampling discretization of integral norms of the hyperbolic cross\n polynomials

2020/05/12 by Vladimir Temlyakov, Temlyakov, Vladimir · 1 citation
Computer Science · #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2005.05967

openalex publication_date 2020/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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