- #1
Euge
Gold Member
MHB
POTW Director
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Here's this week's problem!
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Let $f$ be a holomorphic function on the punctured unit disc $\Bbb D \setminus \{0\}$ such that
\(\displaystyle |f(z)| \le \log \frac{1}{|z|} \quad \text{for all} \quad z \in \Bbb D \setminus \{0\}.\)
Prove that $f \equiv 0$.
_________Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
_________
Let $f$ be a holomorphic function on the punctured unit disc $\Bbb D \setminus \{0\}$ such that
\(\displaystyle |f(z)| \le \log \frac{1}{|z|} \quad \text{for all} \quad z \in \Bbb D \setminus \{0\}.\)
Prove that $f \equiv 0$.
_________Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!