Fitting a Cm-smooth function to data, III

• 成果类型: Article
• 署名作者: Fefferman, Charles
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.427
• 发表日期: 2009
• 页码: 427-441
• 关键词: theorem; sets

摘要

Fix m, n >= 1. Given an N-point set E subset of R-n, we exhibit a list of O(N) subsets S-1, S-2,..., S-L subset of E, each containing O(1) points, such that the following holds: Let f : E -> R-n. Suppose that, for each l = 1,..., L, there exists F-l is an element of C-m (R-n) with norm <= 1, agreeing with f on S-l. Then there exists F is an element of C-m (R-n), with norm O (1), agreeing with f on E. We give an application to the problem of discarding outliers from the set E.