A sharp discrete convolution sum estimate

被引：2
|
作者：
Stynes, Martin [1 ]
Wang, Dongling [2 ,3 ]
机构：
[1] Beijing Computat Sci Res Ctr, Appl & Computat Math Div, Beijing 100193, Peoples R China
[2] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China
[3] Xiangtan Univ, Natl Ctr Appl Math Hunan, Xiangtan 411105, Hunan, Peoples R China
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2023年 / 117卷
基金：
中国国家自然科学基金;
关键词：
Discrete convolution sum; QUADRATURE;
D O I：
10.1016/j.cnsns.2022.106923
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper by C. Lubich in Numer. Math. 2(52):129-145, 1988 is widely cited for its analysis of convolution quadrature rules for integrals with weakly singular kernels. This analysis depends on a key technical lemma (an upper bound on a discrete convolution sum) whose proof uses some advanced tools. In the present paper it will be shown that this lemma can be quickly proved in an elementary way; moreover, the new proof includes those cases that were excluded from the 1988 paper, and the bounds obtained are shown to be sharp.(c) 2022 Elsevier B.V. All rights reserved.
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