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arXiv · 1607.01865

Preasymptotics and asymptotics of approximation numbers of anisotropic Sobolev embeddings

JIa Chen·Heping Wang
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Abstract

In this paper, we obtain the preasymptotic and asymptotic behavior and strong equivalences of the approximation numbers of the embeddings from the anisotropic Sobolev spaces $W_2^{\bf R}(\Bbb T^d)$ to $L_2(\Bbb T^d)$. We also get the preasymptotic behavior of the approximation numbers of the embeddings from the limit spaces $W_2^{\infty}(\Bbb T^d)$ of the anisotropic Sobolev spaces $W_2^{\bf R}(\Bbb T^d)$ to $L_2(\Bbb T^d)$. We show that both the above embedding problems are intractable and do not suffer from the curse of dimensionality.

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JIa Chen, Heping Wang. 2016-07-07. Preasymptotics and asymptotics of approximation numbers of anisotropic Sobolev embeddings. https://arxiv.org/abs/1607.01865

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