A generalized sharp Whitney theorem for jets.

Charles Fefferman

Revista Matemática Iberoamericana (2005)

  • Volume: 21, Issue: 2, page 577-688
  • ISSN: 0213-2230

Abstract

top
Suppose that, for each point x in a given subset E ⊂ Rn, we are given an m-jet f(x) and a convex, symmetric set σ(x) of m-jets at x. We ask whether there exist a function F ∈ Cm,w(Rn) and a finite constant M, such that the m-jet of F at x belongs to f(x) + Mσ(x) for all x ∈ E. We give a necessary and sufficient condition for the existence of such F, M, provided each σ(x) satisfies a condition that we call "Whitnet w-convexity".

How to cite

top

Fefferman, Charles. "A generalized sharp Whitney theorem for jets.." Revista Matemática Iberoamericana 21.2 (2005): 577-688. <http://eudml.org/doc/41944>.

@article{Fefferman2005,
abstract = {Suppose that, for each point x in a given subset E ⊂ Rn, we are given an m-jet f(x) and a convex, symmetric set σ(x) of m-jets at x. We ask whether there exist a function F ∈ Cm,w(Rn) and a finite constant M, such that the m-jet of F at x belongs to f(x) + Mσ(x) for all x ∈ E. We give a necessary and sufficient condition for the existence of such F, M, provided each σ(x) satisfies a condition that we call "Whitnet w-convexity".},
author = {Fefferman, Charles},
journal = {Revista Matemática Iberoamericana},
keywords = {Funciones diferenciables; Jets; Convexidad},
language = {eng},
number = {2},
pages = {577-688},
title = {A generalized sharp Whitney theorem for jets.},
url = {http://eudml.org/doc/41944},
volume = {21},
year = {2005},
}

TY - JOUR
AU - Fefferman, Charles
TI - A generalized sharp Whitney theorem for jets.
JO - Revista Matemática Iberoamericana
PY - 2005
VL - 21
IS - 2
SP - 577
EP - 688
AB - Suppose that, for each point x in a given subset E ⊂ Rn, we are given an m-jet f(x) and a convex, symmetric set σ(x) of m-jets at x. We ask whether there exist a function F ∈ Cm,w(Rn) and a finite constant M, such that the m-jet of F at x belongs to f(x) + Mσ(x) for all x ∈ E. We give a necessary and sufficient condition for the existence of such F, M, provided each σ(x) satisfies a condition that we call "Whitnet w-convexity".
LA - eng
KW - Funciones diferenciables; Jets; Convexidad
UR - http://eudml.org/doc/41944
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.