Analytic extension of differentiable functions defined in closed sets by means of continuous linear operators

Frerick, Leonhard; Vogt, Dietmar

doi:10.1090/S0002-9939-01-06260-8

Analytic extension of differentiable functions defined in closed sets by means of continuous linear operators
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by Leonhard Frerick and Dietmar Vogt PDF

Proc. Amer. Math. Soc. 130 (2002), 1775-1777 Request permission

Abstract:

In this paper we solve the following problem posed by Schmets and Valdivia: Under which conditions does there exist an extension operator from the space ${\mathscr E} (F)$ of the Whitney jets on a closed set $F \subset {\mathbb {R}} ^n$ to ${\mathscr E}({\mathbb {R}}^n)$ so that the extended functions are real analytic outside $F$?

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