Projections and Non‐Linear Approximation in the Space BV(Rd)
Projections and Non‐Linear Approximation in the Space BV(Rd)
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空间 BV(Rd) 中的投影和非线性近似
DOI：
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发表时间：
2003
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通讯作者：
P. Wojtaszczyk
中科院分区：
文献类型：
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作者：
P. Wojtaszczyk
本文的目的是分析Haar系统中的多项式对Rd上d > 1的有界变差函数在Lp-范数p = d /（d − 1）下的非线性逼近。指数p是自然指数，因为它是Sobolev不等式中的正确指数。我们在本文中讨论的近似方案主要与Haar阈值和m项近似有关。这些问题的d = 2详细研究了一份文件科恩，德沃尔，Petrushev和徐。本文的主要目的是将他们的结果推广到d ∈ 2的情形。
The aim of this paper is to provide an analysis of non‐linear approximation in the Lp‐norm p = d / (d − 1) of functions of bounded variation on Rd with d > 1 by polynomials in the Haar system. The exponent p is the natural exponent as it is the correct exponent in the Sobolev inequality. The approximation schemes that we discuss in this paper are mostly related to Haar thresholding and m‐term approximation. These problems for d = 2 are studied in detail in a paper by Cohen, DeVore, Petrushev and Xu. The main aim of this paper is to extend their results to the case d ⩾ 2.