用三角多项式逼近Lip(α, p), (p > 1)-类的信号(函数)

K. Khatri, V. Narayan
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引用次数: 1

摘要

. 给定Lip(α,p) (0 < α 61,p > 1)类中的函数f, Mittal和Singh(2014)通过使用三角多项式来近似这样的f,三角多项式是f的傅里叶级数表示的某些Riesz均值或Nörlund均值变换的第n项。他们证明了近似度为O ((λ (n))−α),并将Leindler(2005)的两个定理进行了推广,其中Leindler将钱德拉(2002)给出的{pn}上的条件弱化为更一般的三角矩阵方法。对于一类更一般的下三角矩阵,我们得到了相同的近似程度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Approximation of signals (functions) of Lip(α, p), (p > 1)-class by trigonometric polynomials
. Given a function f in the class Lip( α,p ) (0 < α 6 1 ,p > 1), Mittal and Singh (2014) approximated such an f by using trigonometric polynomials, which are the n th terms of either certain Riesz mean or Nörlund mean trans-forms of the Fourier series representation for f . They showed that the degree of approximation is O (( λ ( n )) − α ) and extended two theorems of Leindler (2005) where he had weakened the conditions on { p n } given by Chandra (2002) to more general classes of triangular matrix methods. We obtain the same degree of approximation for a more general class of lower triangular matrices.
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