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.

中文翻译：

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双曲交叉多项式积分范数的采样离散化

摘要

本文致力于从给定的有限维子空间离散化函数的积分范数。我们使用抽样离散化的最新一般结果，为双曲交叉频率的多元三角多项式推导新的Marcinkiewicz型离散化定理。结果表明，最近开发的技术使我们可以朝这个方向改进已知的结果。