A short note on the comparison of interpolation widths, entropy numbers, and Kolmogorov widths

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• 作者：Ingo Steinwart ^{ingo.steinwart@mathematik.uni-stuttgart.de}
• 关键词：Interpolation widths ; Kolmogorov widths ; Entropy numbers ; Reproducing kernel Hilbert spaces ; Sobolev spaces
• 刊名：Journal of Approximation Theory
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：215
• 期：Complete
• 页码：13-27
• 全文大小：299 K
• 卷排序：215

文摘

We compare the Kolmogorov and entropy numbers of compact operators mapping from a Hilbert space into a Banach space. These general findings are then applied to embeddings between reproducing kernel Hilbert spaces and L∞(μ)L∞(μ). Here a sufficient condition for a gap of the order n1/2n1/2 between the associated interpolation and Kolmogorov nn-widths is derived. Finally, we show that in the multi-dimensional Sobolev case, this gap actually occurs between the Kolmogorov and approximation widths.