Higher-order tangents and Fefferman's paper on Whitney's extension problem

• 成果类型: Article
• 署名作者: Bierstone, Edward; Milman, Pierre D.; Pawlucki, Wieslaw
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.164.361
• 发表日期: 2006
• 页码: 361-370
• 关键词: differentiable functions; sets

摘要

Whitney [W2] proved that a function defined on a closed subset of R is the restriction of a C-m function if the limiting values of all m(th) divided differences form a continuous function. We show that Fefferman's solution of Whitney's problem for R-n [F, Th. 1] is equivalent to a variant of our conjecture in [BMP2] giving a criterion for C-m extension in terms of iterated limits of finite differences.