QQ客服 官方微博 反馈留言

	ON LAGRANGE INTERPOLATION AT DISTURBED ROOTS OF UNITY
	CHUI, CK ; SHEN, XC ; ZHONG, LF
	1993
关键词	DISTURBED ROOTS OF UNITY MARCINKIEWICZ-ZYGMUND TYPE INEQUALITY LAGRANGE INTERPOLATION ORDER OF APPROXIMATION AP-WEIGHTS HP-INTERPOLATION
英文摘要	Let Z(nk) = e(it)nk, 0 less-than-or-equal-to t(n0) < ... < t(nn) < 2pi , f a function in the disc algebra A , and mu(n) = max{\t(nk) - 2kpi/(n + 1)\: 0 less-than-or-equal-to k less-than-or-equal-to n} . Denote by L(n)(f; .) the polynomial of degree n that agrees with f at {Z(nk): k = 0, ... , n} In this paper, we prove that for every p, 0 < p < infinity, there exists a delta(p) > 0, such that \\L(n)(f; .) - f\\p = O(omega(f; 1/n)) whenever mu(n) less-than-or-equal-to delta(p)/(n + 1) . It must be emphasized that delta(p) necessarily depends on p , in the sense that there exists a family {z(nk): k = 0, ... , n} with mu(n) = delta2/(n + 1) and such that \\L(n)(f; .) - f\\2 = O(omega(f; 1/n)) for all f is-an-element-of A but sup{\\Ln(f; .)\\p: f is-an-element-of A, \\f\\infinity = 1} diverges for sufficiently large values of p. In establishing our estimates, we also derive a Marcinkiewicz-Zygmund type inequality for {Z(nk)}.; Mathematics; SCI(E); 5; ARTICLE; 2; 817-830; 336
语种	英语
出处	SCI
出版者	transactions of the american mathematical society
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/402246]
专题	数学科学学院
推荐引用方式 GB/T 7714	CHUI, CK,SHEN, XC,ZHONG, LF. ON LAGRANGE INTERPOLATION AT DISTURBED ROOTS OF UNITY. 1993-01-01.

个性服务

查看访问统计

相关权益政策

暂无数据

收藏/分享

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。