%0 Journal Article
%T 加权多元Paley-Wiener空间在概率框架和平均框架下的Kolmogorov n-宽度<br>Kolmogorov n-Width of Weighted Multivariate Paley-Wiener Spaces in Probability and Average Settings
%A 罗莹
%J Advances in Applied Mathematics
%P 981-994
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.144221
%X 加权多元Paley-Wiener空间不仅在通讯、信息处理、数据压缩等方面有广泛应用&#65292;而且也是逼近定义在<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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上的函数类的重要工具&#65292;因而得到广泛的深入研究。本文研究加权多元Paley-Wiener空间在概率框架和平均框架下的逼近特征&#65292;特别地&#65292;利用离散化的方法估计了在概率框架和平均框架下&#65292;加权多元Paley-Wiener空间的Kolmogorov n-宽度的精确渐进阶。<br>Weighted multivariate Paley-Wiener spaces have wide applications in communication, information processing, data compression, and other fields. They are also important tools for approximating classes of functions defined on <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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, and thus have been extensively studied. This paper studies the approximation characteristics of weighted multivariate Paley-Wiener spaces in probability and average settings. In particular, by using discretization methods, the paper estimates the exact asymptotic order of the Kolmogorov n-width of weighted multivariate Paley-Wiener spaces in the probability and average settings.
%K 加权多元Paley-Wiener空间&#65292
%K 概率框架&#65292
%K 平均框架&#65292
%K 渐近阶<br>Weighted Multivariate Paley-Wiener Space
%K Probability Setting
%K Average Setting
%K Asymptotic Order
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=113395