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Strong Equivalences of Approximation Numbers and Tractability of Weighted Anisotropic Sobolev Embeddings
Acta Mathematica Scientia ( IF 1.2 ) Pub Date : 2020-10-10 , DOI: 10.1007/s10473-020-0611-x
Jidong Hao , Heping Wang

In this paper, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences ${\bf a}=\{a_j\}_{j\geq1}$ and ${\bf b}=\{b_j\}_{j\geq1}$ of positive numbers. We obtain strong equivalences of the approximation numbers, and necessary and sufficient conditions on ${\bf a}$, ${\bf b}$ to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.

中文翻译:

加权各向异性 Sobolev 嵌入的逼近数和可处理性的强等价

在本文中,我们研究了在加权各向异性 Sobolev 空间上定义的多元近似,该空间依赖于两个序列 ${\bf a}=\{a_j\}_{j\geq1}$ 和 ${\bf b}=\{b_j\ }_{j\geq1}$ 的正数。我们获得了近似数的强等价性,以及 ${\bf a}$, ${\bf b}$ 上的充分必要条件,以实现加权各向异性 Sobolev 嵌入的各种易处理性概念。
更新日期:2020-10-10
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