对称权的最优恢复与广义Carlson不等式

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-07 DOI:10.1016/j.jco.2023.101807

K.Yu. Osipenko

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引用次数: 0

摘要

研究了齐次权加权lq空间中算子从噪声信息中恢复的问题。证明了若干一般定理，并将其应用于若干权重的多维卡尔森型不等式的精确常数的求取，以及噪声傅里叶变换中微分算子的恢复问题。特别地，得到了从lp度规的噪声傅里叶变换中恢复广义拉普拉斯算子幂的最优方法。

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Optimal recovery and generalized Carlson inequality for weights with symmetry properties

The paper concerns problems of the recovery of operators from noisy information in weighted $L_{q}$ -spaces with homogeneous weights. A number of general theorems are proved and applied to finding exact constants in multidimensional Carlson type inequalities with several weights and problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of generalized Laplace operators from a noisy Fourier transform in the $L_{p}$ -metric.

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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.