On weighted Lebesgue function type sums

doi:10.1016/j.jat.2006.11.001

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	On weighted Lebesgue function type sums
	Shi, Ying Guang
	2007-06-01
发表期刊	JOURNAL OF APPROXIMATION THEORY
ISSN	0021-9045
卷号	146 期号:2 页码:243-251
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.
关键词	weighted Lebesgue function type sum Lagrange interpolation orthogonal polynomials
DOI	10.1016/j.jat.2006.11.001
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000247705000006
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4689
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.