Strong equivalences of approximation numbers and tractability of weighted anisotropic Sobolev embeddings

07/01/2019

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by   JiDong Hao, et al.

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In this paper, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a={a_j}_j≥1 and b={b_j}_j≥1 of positive numbers. We obtain strong equivalences of the approximation numbers, and necessary and sufficient conditions on a, b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.