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Suppose $g(z)$ has an isolated singularity at $z=z_0$ and $|\Re[g(z)]| \ge M>0$ for all $z \in \mathbb C-\{z_0\}$. What is the type of singularity of $g$ at $z_0$?

I have a guess it is removable but I could not argue why it can not be a pole though. To rule out essential, I argue with Casorati-Weierstrass theorem.


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    How do you define $\text{Reg} z$, and what is $M$?2012-12-28
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    That's the real part of $g$ and it takes the value outside the strip of $-M$ to $M$2012-12-28
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    I've edited the LaTeX. Now, what is the question? You have given an assumption, but what would you like us to do with that assumption?2012-12-28
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    @FlybyNight, I am sorry, I need to figure out what kind of singularity does $g$ have at $z_0$?2012-12-28

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