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

• Autores: Wieslawa Pawlucki, Edward Bierstone, Pierre D. Milman
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 164, Nº 1, 2006, págs. 361-370
• Idioma: inglés
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• Resumen

  • Whitney [W2] proved that a function defined on a closed subset of R is the restriction of a Cm function if the limiting values of all mth divided differences form a continuous function. We show that Fefferman¿s solution of Whitney¿s problem for Rn [F, Th. 1] is equivalent to a variant of our conjecture in [BMP2] giving a criterion for Cm extension in terms of iterated limits of finite differences.