Suppose that $f$ is an entire function of exponential type, i.e., there exist constants $A$ and $B$ such that \begin{equation*} |f(z)| \le A e^{B|z|} \end{equation*} for all complex $z$. Prove that if $f$ is bounded on two nonparallel lines, then it must be a constant. I think it may be related to the Paley and Wiener Theorem, but I have no idea how anyway. Can anyone help?
2026-03-27 17:51:49.1774633909
An entire function of exponential type on nonparallel lines.
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