Tagged Questions
9
votes
1answer
239 views
Show that f is a polynomial
Suppose $f$ is an entire function on $\mathbb{C}^n$ that satisfies for every $\epsilon>0$ a growth-condition $$|f(z)|\leq C_{\epsilon}(1+|z|)^{N_{\epsilon}}e^{\epsilon |
\text{Im}\,z|}$$
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3
votes
1answer
166 views
holomorphic function is real analytic?
$f$ is a holomorphic function on $\mathbb C^n$. If we regard $f$ as a function $F$ from $\mathbb R^{2n} \to \mathbb R^2$, is it necessarily that $F$ is real analytic?
