PeterM

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seen Mar 25 at 0:30
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Mar
25
 accepted Suppose $|\alpha_1| \le |\alpha_2| \le \cdots \le 1$, $n(r) = \#\{\alpha_j \le r\}$. Prove $\int_0^1n(r)dr = \sum_{j=1}^\infty(1-|\alpha_j|)$.
Mar
24
 revised Suppose $|\alpha_1| \le |\alpha_2| \le \cdots \le 1$, $n(r) = \#\{\alpha_j \le r\}$. Prove $\int_0^1n(r)dr = \sum_{j=1}^\infty(1-|\alpha_j|)$.
added 30 characters in body
Mar
24
 asked Suppose $f\in H(U), f(U) \subseteq U$. How many zeros can $f$ have in the disc $D(0,\beta)$?
Mar
24
 asked Suppose $|\alpha_1| \le |\alpha_2| \le \cdots \le 1$, $n(r) = \#\{\alpha_j \le r\}$. Prove $\int_0^1n(r)dr = \sum_{j=1}^\infty(1-|\alpha_j|)$.
Mar
7
 accepted Characterization of one-to-one conformal mapping from unit disc onto a square
Mar
7
 comment Characterization of one-to-one conformal mapping from unit disc onto a square
I applied Schwarz lemma and solved the general case with ease. Thank you!
Mar
6
 asked Characterization of one-to-one conformal mapping from unit disc onto a square
Mar
6
 comment Maximize absolute value of complex logarithm
Great answer. The hyperbolic metric section is fascinating. Ahlfors doesn't cover it either. What should I study to learn more about it?
Mar
6
 accepted Maximize absolute value of complex logarithm
Mar
3
 comment Maximize absolute value of complex logarithm
@mrf Thanks for your comment. I had a mistake in the problem statement. It's actually $|\Re(g)| < 1$ (with an absolute value).
Mar
3
 revised Maximize absolute value of complex logarithm
added 2 characters in body
Mar
3
 asked Maximize absolute value of complex logarithm
Mar
2
 awarded  Teacher
Mar
2
 accepted Finding a trigonometric polynomial
Mar
2
 answered Finding a trigonometric polynomial
Mar
2
 comment If $f,g: U \rightarrow \Omega$ are holomorphic, $f(0)=g(0)$ and $f$ is 1-1&onto, then $f$ has larger image of a disk than that of $g$.
@richard Got it. Thank you!
Mar
2
 comment Limits of complex function in a strip
I can't for the life of me figure out why $f_n\to 0$. I understand that every sequence has a subsequence $\to 0$. But why is $f_n \to 0$. Thanks.
Feb
28
 comment Finding a trigonometric polynomial
@5pm Gotcha. Thanks!!
Feb
28
 comment If $f,g: U \rightarrow \Omega$ are holomorphic, $f(0)=g(0)$ and $f$ is 1-1&onto, then $f$ has larger image of a disk than that of $g$.
@richard Schwarz lemma gave me $|f^{-1}\circ g(z)| < |z|$. I thought of applying $f$ to both sides to reach |g(z)| < |f(z)| and prove the exercise. I don't know what else to do. Thanks.
Feb
28
 asked Finding a trigonometric polynomial
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