On the cardinality of lower sets and universal discretization

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-01 DOI:10.1016/j.jco.2022.101726

F. Dai , A. Prymak , A. Shadrin , V.N. Temlyakov , S. Tikhonov

引用次数: 0

Abstract

A set Q in $Z_{+}^{d}$ is a lower set if $(k_{1}, \dots, k_{d}) \in Q$ implies $(l_{1}, \dots, l_{d}) \in Q$ whenever $0 \leq l_{i} \leq k_{i}$ for all i. We derive new and refine known results regarding the cardinality of the lower sets of size n in $Z_{+}^{d}$ . Next we apply these results for universal discretization of the $L_{2}$ -norm of elements from n-dimensional subspaces of trigonometric polynomials generated by lower sets.

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下集的基数性与泛离散化

如果（k1，…，kd）∈Q对所有i意味着（l1，…，ld）∈Q，只要0≤li≤ki。我们导出了关于Z+d中大小为n的较低集合的基数的新的和改进的已知结果。接下来，我们将这些结果应用于由较低集合生成的三角多项式的n维子空间的元素的L2范数的通用离散化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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