lp,0的负定理

Ghazi Abdullah Madlol
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引用次数: 0

摘要

对于一个给定的非负整数n,我们可以找到一个单调函数f取决于n,定义在区间I =[1],和绝对的常数c > 0,满足以下关系:(2 a€-E_n我(f)一个€-_p) / (n + 1) ^ 3‰¤一个€-E_ (n + 1) ^ 1 (f)€-_pa‰¤ca€-E_n我(f)一个€-_p,一个€-E_ (n + 1) ^ 1 (f)€-_p的程度是最好的Lp单调函数的近似代数多项式的程度不超过n + 1。ã€-E_n (f Ì′)ã€-_p是f Ì′通过阶数不超过n的代数多项式的最佳Lp逼近的阶数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
NEGATIVE THEOREM FOR LP,0
For a given nonnegative integer number n, we can find a monotone function f depending on n, defined on the interval I=[-1,1], and an absolute constant c>0, satisfying the following relationship: (2〖E_n (f ́ )〗_p)/(n+1)^3 ≤〖E_(n+1)^1 (f)〗_p≤c〖E_n (f ́ )〗_p, where 〖E_(n+1)^1 (f)〗_p is the degree of the best Lp monotone approximation of the function f by algebraic polynomial of degree not exceeding n+1. 〖E_n (f ́ )〗_p is the degree of the best Lp approximation of the function f ́ by algebraic polynomial of degree not exceeding n.
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