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

JOURNAL OF APPROXIMATION THEORY

卷:215

Article

Steinwart, Ingo¹ 

[1] Univ Stuttgart, Fac Math & Phys 8, Inst Stochast & Applicat, D-70569 Stuttgart, Germany

关键词: Interpolation widths;    Kolmogorov widths;    Entropy numbers;    Reproducing kernel Hilbert spaces;    Sobolev spaces;   

DOI  :  10.1016/j.jat.2016.11.006

来源: Elsevier

【 摘 要 】

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 Loo (A). Here a sufficient condition for a gap of the order n(1/2) between the associated interpolation and Kolmogorov n-widths is derived. Finally, we show that in the multi-dimensional Sobolev case, this gap actually occurs between the Kolmogorov and approximation widths. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free