Mean convergence of Hermite-Fejer interpolation based on the zeros of Lascenov polynomials

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	Mean convergence of Hermite-Fejer interpolation based on the zeros of Lascenov polynomials
	Shi, YG
	1996-03-01
发表期刊	CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
ISSN	0008-4395
卷号	39 期号:1 页码:117-128
摘要	Weighted LP mean convergence of Hermite-Fejer interpolation based on the zeros of orthogonal polynomials with respect to the weight \x\(2 alpha+1)(1 - x(2))(beta) (alpha,beta > - 1) is investigated. A necessary and sufficient condition for such convergence for all continuous functions is given. Meanwhile divergence of Hermite-Fejer interpolation in L(p) with p > 2 is obtained. This gives a possible answer to Problem 17 of P. Turan [J. Approx. Theory, 29(1980), p. 40].
关键词	Hermite-Fejer interpolation mean convergence orthogonal polynomials
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:A1996UF60000016
出版者	CANADIAN MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13191
专题	中国科学院数学与系统科学研究院
作者单位	CHINESE ACAD SCI, INST COMPUTAT MATH & SCI ENGN COMP, BEIJING 100080, PEOPLES R CHINA
推荐引用方式 GB/T 7714	Shi, YG. Mean convergence of Hermite-Fejer interpolation based on the zeros of Lascenov polynomials[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES,1996,39(1):117-128.
APA	Shi, YG.(1996).Mean convergence of Hermite-Fejer interpolation based on the zeros of Lascenov polynomials.CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES,39(1),117-128.
MLA	Shi, YG."Mean convergence of Hermite-Fejer interpolation based on the zeros of Lascenov polynomials".CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES 39.1(1996):117-128.