函数的平滑性和近似过程的平滑性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-03-01 DOI:10.1142/s1664360720300029

Yurii Kolomoitsev, S. Tikhonov

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引用次数: 9

摘要

我们提供了一个全面的研究之间的相互关系的不同措施的光滑的函数在不同的领域和光滑的近似过程的性质。有两种一般的方法来解决这个问题:第一种是基于Banach空间的几何性质，第二种是基于Littlewood-Paley定理和Hörmander-type乘数定理。特别地，我们得到了由[公式:见原文]给出的光滑测度的新的尖锐不等式——光滑的泛函或模。作为近似过程的例子，我们考虑了最佳多项式和样条近似，傅里叶乘数算子在[公式:见文]，[公式:见文]，[公式:见文]，非线性小波近似等。

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Smoothness of functions versus smoothness of approximation processes

We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed: The first based on geometric properties of Banach spaces and the second on Littlewood–Paley and Hörmander-type multiplier theorems. In particular, we obtain new sharp inequalities for measures of smoothness given by the [Formula: see text]-functionals or moduli of smoothness. As examples of approximation processes we consider best polynomial and spline approximations, Fourier multiplier operators on [Formula: see text], [Formula: see text], [Formula: see text], nonlinear wavelet approximation, etc.

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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.