A problem about almost-periodic sequences
- Greetings, everybody!
This is not exactly a harmonic analysis problem but, I hope,
it is OK to ask somewhat "off-topic" questions here now and then.
Assume that $f_n$ ($-\infty<n<+\infty$)is a sequence of analytic
in the unit disk and continuous up to the boundary functions.
Suppose that the sequence $f_n(z)$ is almost periodic for every
$z$ on the unit circumference. Does it imply that the sequence
$f_n(0)$ is almost periodic as well?