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。
修改评论