Suppose $f$ is $C$-analytic in $|z| ≤ 1$, $f ≪ 2$ for $|z| = 1$, Im $z ≥ 0$ and $f ≪ 3$ for $|z| = 1$, Im $z ≤ 0$. Show then that $| f (0)| ≤ \sqrt{6}$.
I know to consider $f(z)f(-z)$ but not sure where to go from here. How can I prove this ?
2025-01-12 23:51:15.1736725875
Show that $| f (0)| ≤ \sqrt{6}$
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