Every compact set in ūĚźā n is a good compact set
Annales de l'Institut Fourier, Volume 20 (1970) no. 1, pp. 493-498.

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.

Soit K un compact d‚Äôun ouvert V dans C n . On d√©montre l‚Äôexistence d‚Äôun voisinage U de K qui satisfait la condition suivante¬†: si f est holomorphe sur V et s‚Äôil existe une suite des polynomes qui approchent f uniform√©ment sur un voisinage ouvert U f de K, il existe une suite de polyn√īmes qui approchent f uniform√©ment sur U

@article{AIF_1970__20_1_493_0,
     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},
     volume = {20},
     number = {1},
     year = {1970},
     doi = {10.5802/aif.348},
     zbl = {0188.39003},
     mrnumber = {41 #7154},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.348/}
}
TY  - JOUR
AU  - Björk, Jan Erik
TI  - Every compact set in ${\bf C}^n$ is a good compact set
JO  - Annales de l'Institut Fourier
PY  - 1970
DA  - 1970///
SP  - 493
EP  - 498
VL  - 20
IS  - 1
PB  - Institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.348/
UR  - https://zbmath.org/?q=an%3A0188.39003
UR  - https://www.ams.org/mathscinet-getitem?mr=41 #7154
UR  - https://doi.org/10.5802/aif.348
DO  - 10.5802/aif.348
LA  - en
ID  - AIF_1970__20_1_493_0
ER  - 
%0 Journal Article
%A Björk, Jan Erik
%T Every compact set in ${\bf C}^n$ is a good compact set
%J Annales de l'Institut Fourier
%D 1970
%P 493-498
%V 20
%N 1
%I Institut Fourier
%U https://doi.org/10.5802/aif.348
%R 10.5802/aif.348
%G en
%F AIF_1970__20_1_493_0
Björk, Jan Erik. Every compact set in ${\bf C}^n$ is a good compact set. Annales de l'Institut Fourier, Volume 20 (1970) no. 1, pp. 493-498. doi : 10.5802/aif.348. http://archive.numdam.org/articles/10.5802/aif.348/

[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

Cited by Sources: