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Strong Equivalences of Approximation Numbers and Tractability of Weighted Anisotropic Sobolev Embeddings

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Abstract

In this article, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a = {aj}j≥1 and b = {bj}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.

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Correspondence to Heping Wang.

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Supported by the National Natural Science Foundation of China (11671271) and the Natural Science Foundation of Beijing Municipality (1172004).

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Hao, J., Wang, H. Strong Equivalences of Approximation Numbers and Tractability of Weighted Anisotropic Sobolev Embeddings. Acta Math Sci 40, 1765–1782 (2020). https://doi.org/10.1007/s10473-020-0611-x

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  • DOI: https://doi.org/10.1007/s10473-020-0611-x

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