On extensions of holomorphic functions satisfying a polynomial growth condition on algebraic varieties in ${𝐂}^n$

Björk, Jean Erik. "On extensions of holomorphic functions satisfying a polynomial growth condition on algebraic varieties in ${\bf C}^n$." Annales de l'institut Fourier 24.4 (1974): 157-165. <http://eudml.org/doc/74195>.

@article{Björk1974,
abstract = {Let $V$ be an algebraic variety in $C^n$ and when $k\ge 0$ is an integer then $\{\rm Pol\}\, (V,k)$ denotes all holomorphic functions $f(z)$ on $V$ satisfying $\vert f(z)\vert \le C_f(1+\vert z\vert )^k$ for all $z\in V$ and some constant $C_f$. We estimate the least integer $\varepsilon (V,k)$ such that every $f\in \,\{\rm Pol\}\,(V,k)$ admits an extension from $V$ into $C^n$ by a polynomial $P(z_1,\ldots ,z_n)$, of degree $k+\varepsilon (V,k)$ at most. In particular $\lim _\{k&gt;\infty \}\varepsilon (V,k)$ is related to cohomology groups with coefficients in coherent analytic sheaves on $V$. The existence of the finite integer $\varepsilon (V,k)$ is for example an easy consequence of Kodaira’s Vanishing Theorem.},
author = {Björk, Jean Erik},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {4},
pages = {157-165},
publisher = {Association des Annales de l'Institut Fourier},
title = {On extensions of holomorphic functions satisfying a polynomial growth condition on algebraic varieties in $\{\bf C\}^n$},
url = {http://eudml.org/doc/74195},
volume = {24},
year = {1974},
}

TY - JOUR
AU - Björk, Jean Erik
TI - On extensions of holomorphic functions satisfying a polynomial growth condition on algebraic varieties in ${\bf C}^n$
JO - Annales de l'institut Fourier
PY - 1974
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 4
SP - 157
EP - 165
AB - Let $V$ be an algebraic variety in $C^n$ and when $k\ge 0$ is an integer then ${\rm Pol}\, (V,k)$ denotes all holomorphic functions $f(z)$ on $V$ satisfying $\vert f(z)\vert \le C_f(1+\vert z\vert )^k$ for all $z\in V$ and some constant $C_f$. We estimate the least integer $\varepsilon (V,k)$ such that every $f\in \,{\rm Pol}\,(V,k)$ admits an extension from $V$ into $C^n$ by a polynomial $P(z_1,\ldots ,z_n)$, of degree $k+\varepsilon (V,k)$ at most. In particular $\lim _{k&gt;\infty }\varepsilon (V,k)$ is related to cohomology groups with coefficients in coherent analytic sheaves on $V$. The existence of the finite integer $\varepsilon (V,k)$ is for example an easy consequence of Kodaira’s Vanishing Theorem.
LA - eng
UR - http://eudml.org/doc/74195
ER -