下集的基数性与泛离散化

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

摘要

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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On the cardinality of lower sets and universal discretization

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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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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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