Best N Term Approximation Spaces for Tensor Product Wavelet Bases

被引：0
|
作者：
Pal-Andrej Nitsche
机构：
[1] Seminar for Applied Mathematics,
[2] ETH-Zentrum,undefined
[3] CH-8092 Zurich,undefined
来源：
Constructive Approximation | 2006年 / 24卷
关键词：
Best N term approximation; Tensor product approximation; Sparse grids; Besov spaces;
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学科分类号：
摘要：
We consider best N term approximation using anisotropic tensor product wavelet bases ("sparse grids"). We introduce a tensor product structure ⊗q on certain quasi-Banach spaces. We prove that the approximation spaces Aαq(L2) and Aαq(H1) equal tensor products of Besov spaces Bαq(Lq), e.g., Aαq(L2([0,1]d)) = Bαq(Lq([0,1])) ⊗q · ⊗q Bαq · ·(Lq([0,1])). Solutions to elliptic partial differential equations on polygonal/polyhedral domains belong to these new scales of Besov spaces.
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页码：49 / 70
页数：21
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