- Thread starter
- Moderator
- #1

- Jun 20, 2014

- 1,892

Here is this week's POTW:

-----

Suppose $a$ is a fixed complex number in the open unit disk $\Bbb D$. Consider the holomorphic mapping $\phi : \Bbb D \to \Bbb D$ given by $\phi(z) := (z - a)/(1 - \bar{a}z)$. Find, with proof, the average value of $\left\lvert\frac{d\phi}{dz}\right\rvert^2$ over $\Bbb D$, i.e., the integral $$\frac{1}{\pi}\iint_{\Bbb D} |\phi'(x + yi)|^2\, dx\, dy$$

-----

Remember to read the POTW submission guidelines to find out how to submit your answers!

-----

Suppose $a$ is a fixed complex number in the open unit disk $\Bbb D$. Consider the holomorphic mapping $\phi : \Bbb D \to \Bbb D$ given by $\phi(z) := (z - a)/(1 - \bar{a}z)$. Find, with proof, the average value of $\left\lvert\frac{d\phi}{dz}\right\rvert^2$ over $\Bbb D$, i.e., the integral $$\frac{1}{\pi}\iint_{\Bbb D} |\phi'(x + yi)|^2\, dx\, dy$$

-----

Remember to read the POTW submission guidelines to find out how to submit your answers!

Last edited: