Abstract
In this paper, using an equivalent characterization of the Besov space by its wavelet coefficients and the discretization technique due to Maiorov, we determine the asymptotic degree of the Bernstein n-widths of the compact embeddings
, where \(B_{q_0 }^{s + t} (L_{p_0 } (\Omega ))\) is a Besov space defined on the bounded Lipschitz domain Ω ⊂ ℝd. The results we obtained here are just dual to the known results of Kolmogorov widths on the related classes of functions.
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The first author is supported by Natural Science Foundation of Inner Mongolia (Grant No. 2011MS0103); the second author is supported by National Natural Science Foundation of China (Grant No. 10671019)
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Li, Y.W., Fang, G.S. Bernstein n-widths of Besov embeddings on Lipschitz domains. Acta. Math. Sin.-English Ser. 29, 2283–2294 (2013). https://doi.org/10.1007/s10114-013-2212-2
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DOI: https://doi.org/10.1007/s10114-013-2212-2