最佳恢复和容量估计

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-17 DOI:10.1016/j.jco.2023.101780

Alexander Kushpel

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引用次数: 0

摘要

研究了由概率空间上的正交系统诱导的Rn中凸原点对称体的截面体积。该方法基于John-Löwner椭球体的体积估计和各自系统引起的规范期望。得到的估计使我们能够建立截面半径的下界，从而给出Gelfand宽度(或线性宽度)的下界。作为应用，我们给出了一种新的求乘子算子的Gelfand宽度和Kolmogorov宽度的方法。特别地，我们在两点齐次空间上，即当1<q≤p≤∞的困难情况下，建立了Lq上标准Sobolev类Wpγ， γ>0的宽度的尖锐阶。

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Optimal recovery and volume estimates

We study volumes of sections of convex origin-symmetric bodies in $R^{n}$ induced by orthonormal systems on probability spaces. The approach is based on volume estimates of John-Löwner ellipsoids and expectations of norms induced by the respective systems. The estimates obtained allow us to establish lower bounds for the radii of sections which gives lower bounds for Gelfand widths (or linear cowidths). As an application we offer a new method of evaluation of Gelfand and Kolmogorov widths of multiplier operators. In particular, we establish sharp orders of widths of standard Sobolev classes $W_{p}^{γ}$ , $γ > 0$ in $L_{q}$ on two-point homogeneous spaces in the difficult case, i.e. if $1 < q \leq p \leq \infty$ .

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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.