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## Homework Statement

Find a function [tex] g [/tex] analytic in [tex]|z|\leq 2[/tex], with [tex] g(2/3)=0[/tex] and [tex] |g(z)|= 1 [/tex] on [tex]|z|=2[/tex]

## Homework Equations

Bilinear maps

[tex] B_{\alpha}(z)=\frac{z-\alpha}{1-\overline{\alpha}z} [/tex]

[tex] |B_{\alpha}(z)|=1[/tex] on [tex]|z|=1[/tex]

## The Attempt at a Solution

I tried using the maximum modulus theorem but I did not manage to find such a function.