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

Annales de l'institut Fourier (1970)

- Volume: 20, Issue: 1, page 493-498
- ISSN: 0373-0956

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topBjörk, Jan Erik. "Every compact set in ${\bf C}^n$ is a good compact set." Annales de l'institut Fourier 20.1 (1970): 493-498. <http://eudml.org/doc/74010>.

@article{Björk1970,

abstract = {Let $K$ be an compact subset of an open set $V$ in $\{\bf C\}^n$. 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 $U$.},

author = {Björk, Jan Erik},

journal = {Annales de l'institut Fourier},

keywords = {complex functions},

language = {eng},

number = {1},

pages = {493-498},

publisher = {Association des Annales de l'Institut Fourier},

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

url = {http://eudml.org/doc/74010},

volume = {20},

year = {1970},

}

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

PB - Association des Annales de l'Institut Fourier

VL - 20

IS - 1

SP - 493

EP - 498

AB - Let $K$ be an compact subset of an open set $V$ in ${\bf C}^n$. 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 $U$.

LA - eng

KW - complex functions

UR - http://eudml.org/doc/74010

ER -

## References

top- [1] A. MARTINEAU, Sur les fonctionnelles analytiques et la transformation de Fourier-Borel, J. Analyse Math. 9, 1-164 (1963). Zbl0124.31804MR28 #2437
- [2] GUNNIG-ROSSI, Analytic functions of several complex variables, Prentice Hall (1965). Zbl0141.08601

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