Every compact set in ${\bf C}^n$ is a good compact set

Björk, Jan Erik

doi:10.5802/aif.348

Every compact set in

𝐂^{n}

is a good compact set

Björk, Jan Erik

Annales de l'Institut Fourier, Tome 20 (1970) no. 1, pp. 493-498.

Résumé
Abstract

Soit $K$ un compact d’un ouvert $V$ dans $C^{n}$ . On démontre l’existence d’un voisinage $U$ de $K$ qui satisfait la condition suivante : si $f$ est holomorphe sur $V$ et s’il existe une suite des polynomes qui approchent $f$ uniformément sur un voisinage ouvert $U_{f}$ de $K$ , il existe une suite de polynômes qui approchent $f$ uniformément sur $U$

Let $K$ be an compact subset of an open set $V$ in $C^{n}$ . We show the existence of an open neighborhood $U$ of $K$ satisfying the following condition : if $f$ is holomorphic in $V$ and if there exists a sequence of polynomials which approximate $f$ uniformly in some open neighborhood $U_{f}$ of $K$ , there exists a sequence of polynomial which approximate $f$ uniformly in $U$ .

MR Zbl | 1 citation dans Numdam

DOI : 10.5802/aif.348

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     author = {Bj\"ork, Jan Erik},
     title = {Every compact set in ${\bf C}^n$ is a good compact set},
     journal = {Annales de l'Institut Fourier},
     pages = {493--498},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {20},
     number = {1},
     year = {1970},
     doi = {10.5802/aif.348},
     mrnumber = {41 #7154},
     zbl = {0188.39003},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.348/}
}

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Björk, Jan Erik. Every compact set in ${\bf C}^n$ is a good compact set. Annales de l'Institut Fourier, Tome 20 (1970) no. 1, pp. 493-498. doi : 10.5802/aif.348. http://archive.numdam.org/articles/10.5802/aif.348/

Bibliographie
Cité par

[1] A. Martineau, Sur les fonctionnelles analytiques et la transformation de Fourier-Borel, J. Analyse Math. 9, 1-164 (1963). | MR | Zbl

[2] Gunnig-Rossi, Analytic functions of several complex variables, Prentice Hall (1965). | Zbl

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