Average B-width and infinite dimensional G-width of some smooth function classes on the line |
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Authors: | Jiang Yangjie Liu Yongping |
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Affiliation: | (1) North Electric Power University, 071000 Baoding, China;(2) Beijing Narmal University, 100875 Beijing, China |
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Abstract: | In this paper, we get the exact values of average σ-B width and infinite dimensional σ-G width of Sobolev class Br p(R) in the metric Lp(R) (1≤p≤∞) and obtain the exact (σ∈N) and strong asymptotic (σ>1) results of infinite dimensional σ-G widths of Sobolev-Wiener class Wr pq (R) in the metric Lq(R) and its dual case Wr p(R) in the metric Lqp(R) (1≤q≤p≤∞). Supported by the National Natural Science Foundation of China (No. 19671012) and by the Doctoral Programme Foundation of Institution of Higher Education of National Education Committee of China. |
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