The Approximation Characteristics of Weighted Band-Limited Function Space

Yue Li, Guanggui Chen, Yanyan Xu () and Xiangyu Pan
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Yue Li: School of Science, Xihua University, Chengdu 610039, China
Guanggui Chen: Yibin Campus, Xihua University, Yibin 644005, China
Yanyan Xu: School of Science, Xihua University, Chengdu 610039, China
Xiangyu Pan: School of Science, Xihua University, Chengdu 610039, China

Mathematics, 2024, vol. 12, issue 9, 1-16

Abstract: This article primarily investigates the width problem within weighted band-limited function space in a uniform setting. Through an analysis of the properties of s-numbers, we establish a connection between the widths of weighted band-limited function spaces and the s-numbers of infinite-dimensional diagonal operators. Furthermore, employing the discretization method, we estimate the exact asymptotic orders of Kolmogorov n -width and linear n -width in the weighted band-limited function space, which is characterized by the weight ω = ω k = | k | r k ∈ Z 0 .

Keywords: band-limited; s-number; diagonal operators; n-width (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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