A Generalized Sharp Whitney Theorem for Jets

Autores: Charles L. Fefferman
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 21, Nº 2, 2005, págs. 577-688
Idioma: inglés
DOI: 10.4171/rmi/430
Títulos paralelos:
- Un teorema preciso generalizado de Whitney para jets.
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Resumen
- Suppose that, for each point x in a given subset E Ì Rn, we are given an m-jet f(x) and a convex, symmetric set ?(x) of m-jets at x. We ask whether there exist a function F Î Cm,w(Rn) and a finite constant M, such that the m-jet of F at x belongs to f(x) + M?(x) for all x Î E. We give a necessary and sufficient condition for the existence of such F, M, provided each ?(x) satisfies a condition that we call "Whitnet w-convexity".