On weighted Lebesgue function type sums | |
Shi, Ying Guang | |
刊名 | JOURNAL OF APPROXIMATION THEORY
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2007-06-01 | |
卷号 | 146期号:2页码:243-251 |
关键词 | weighted Lebesgue function type sum Lagrange interpolation orthogonal polynomials |
ISSN号 | 0021-9045 |
DOI | 10.1016/j.jat.2006.11.001 |
英文摘要 | Let I be a finite or infinite interval and d mu a measure on I. Assume that the weight function w(x) > 0, w'(x) exists, and the function w'(x)/w(x) is non-increasing on I. Denote by l(k)'s the fundamental polynomials of Lagrange interpolation on a set of nodes x(1)< x(2) < (...) < x(n) in I. The weighted Lebesgue function type sum for l <= i < j <= n and s >= l is defined by S-n(x) = (j)Sigma(k=i)vertical bar(x - x(k))l(k)(x)w(x)/w(x(k))vertical bar(s) In this paper the exact lower bounds of S-n(x) on a "big set" of I and integral(I) S-n(x) d mu(x) are obtained. Some applications are also given. (c) 2007 Elsevier Inc. All rights reserved. |
语种 | 英语 |
出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
WOS记录号 | WOS:000247705000006 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/4688] ![]() |
专题 | 中国科学院数学与系统科学研究院 |
通讯作者 | Shi, Ying Guang |
作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100080, Peoples R China 2.Hunan Normal Univ, Dept Math, Changsha, Peoples R China |
推荐引用方式 GB/T 7714 | Shi, Ying Guang. On weighted Lebesgue function type sums[J]. JOURNAL OF APPROXIMATION THEORY,2007,146(2):243-251. |
APA | Shi, Ying Guang.(2007).On weighted Lebesgue function type sums.JOURNAL OF APPROXIMATION THEORY,146(2),243-251. |
MLA | Shi, Ying Guang."On weighted Lebesgue function type sums".JOURNAL OF APPROXIMATION THEORY 146.2(2007):243-251. |
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