| Version 2 |
Version 1 |
| \theoremstyle{definition} |
\theoremstyle{definition} |
| \newtheorem*{defn}{Definition} |
\newtheorem*{defn}{Definition} |
|
|
| \begin{defn} |
\begin{defn} |
| A function $W\colon {\mathbb{C}}^n \to {\mathbb{C}}$ of the form |
A function $W\colon {\mathbb{C}}^n \to {\mathbb{C}}$ of the form |
| \begin{equation*} |
\begin{equation*} |
| W(z_1,\ldots,z_n) = z_n^m + \sum_{j=1}^{m-1}a_j(z_1,\ldots,z_{n-1})z_n^j , |
W(z_1,\ldots,z_n) = z_n^m + \sum_{j=1}^{m-1}a_j(z_1,\ldots,z_{n-1})z_n^j , |
| \end{equation*} |
\end{equation*} |
|
where the $a_j$ are holomorphic functions in a neighbourhood of the origin, which vanish at the origin,
|
where the $a_j$ are holomorphic functions in a neighbourhood of the origin, the origin,
|
| is called a {\em Weierstrass polynomial}. |
is called a {\em Weierstrass polynomial}. |
| \end{defn} |
\end{defn} |
|
|
| \begin{thebibliography}{9} |
\begin{thebibliography}{9} |
| \bibitem{Hormander:several} |
\bibitem{Hormander:several} |
| Lars H\"ormander. |
Lars H\"ormander. |
| {\em \PMlinkescapetext{An Introduction to Complex Analysis in Several |
{\em \PMlinkescapetext{An Introduction to Complex Analysis in Several |
| Variables}}, |
Variables}}, |
| North-Holland Publishing Company, New York, New York, 1973. |
North-Holland Publishing Company, New York, New York, 1973. |
| \bibitem{Krantz:several} |
\bibitem{Krantz:several} |
| Steven~G.\@ Krantz. |
Steven~G.\@ Krantz. |
| {\em \PMlinkescapetext{Function Theory of Several Complex Variables}}, |
{\em \PMlinkescapetext{Function Theory of Several Complex Variables}}, |
| AMS Chelsea Publishing, Providence, Rhode Island, 1992. |
AMS Chelsea Publishing, Providence, Rhode Island, 1992. |
| \end{thebibliography} |
\end{thebibliography} |
