%0 Journal Article
%T 具有特殊权重的Paley-Wiener空间上的线性宽度问题<br>Linear Width Problem of Paley-Wiener Spaces with Special Weights
%A 罗莹
%J Advances in Applied Mathematics
%P 133-145
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.145242
%X 带有限函数空间在数值分析、数据拟合等方面有广泛的应用&#65292;为许多问题提供了稳定性和可控性&#65292;能够有效地处理近似问题&#65292;找到最佳逼近方案。Paley-Wiener空间作为带有限函数空间的特殊情况&#65292;也是广泛应用于分析和信号处理等领域。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空间的线性n-宽度的精确渐进阶。<br>Spaces of bounded functions have wide applications in numerical analysis, data fitting, and other fields. They provide stability and controllability for many problems, effectively handling approximation problems and finding optimal approximation solutions. As a special case of spaces of bounded functions, Paley-Wiener spaces are also widely used in fields such as analysis and signal processing. This paper studies the approximation properties of weighted multivariate Paley-Wiener spaces in probability and average settings. Specifically, by using discretization methods, it estimates the exact asymptotic order of the linear n-width of weighted multivariate Paley-Wiener spaces in both the probabilistic 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 线性n-宽度<br>Weighted Multivariate Paley-Wiener Space
%K Probability Settings
%K Average Settings
%K Linear n-Width
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=114419