平滑类的近似问题

IF 1.2 4区 数学 Q1 MATHEMATICS Acta Mathematica Scientia Pub Date : 2024-08-27 DOI:10.1007/s10473-024-0505-4
Yongping Liu, Man Lu
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引用次数: 0

摘要

本文研究了 2π 周期光滑类在\(\widetilde{L}_{q}\)中的相对柯尔莫哥洛夫 n 宽。我们估计了 \(\widetilde{W}^{r}H^{\omega}_{p}\) 及其广义类 KpHω (Pr) 的相对宽度,其中 KpHω (Pr) 是由$$P_{r}(t):= t^{sigma} Pi_{j=1}^{l}(t^{2}- t_{j}^{2}),~t_{j} > 0,~j=1, 2,\cdots, l,~l \geq 1,~\sigma \geq 1,~r=2l+\sigma.另外,r-th导数或r-th自共轭微分的连续性模数不超过给定的连续性模数ω。然后我们得到渐近结果,尤其是 p = ∞, 1 ≤ q ≤ ∞ 的情况。
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Approximation problems on the smoothness classes

This paper investigates the relative Kolmogorov n-widths of 2π-periodic smooth classes in \(\widetilde{L}_{q}\). We estimate the relative widths of \(\widetilde{W}^{r}H^{\omega}_{p}\) and its generalized class KpHω (Pr), where KpHω (Pr) is defined by a self-conjugate differential operator Pr (D) induced by

$$P_{r}(t):= t^{\sigma} \Pi_{j=1}^{l}(t^{2}- t_{j}^{2}),~t_{j} > 0,~j=1, 2,\cdots, l,~l \geq 1,~\sigma \geq 1,~r=2l+\sigma.$$

Also, the modulus of continuity of the r-th derivative, or r-th self-conjugate differential, does not exceed a given modulus of continuity ω. Then we obtain the asymptotic results, especially for the case p = ∞, 1 ≤ q ≤ ∞.

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来源期刊
CiteScore
2.00
自引率
10.00%
发文量
2614
审稿时长
6 months
期刊介绍: Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
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