Find all analytic functions in |z|<3 satisfying f(i)=-3i and |f(z)|<=3.
Can I have some ideas on how to solve this question? Thank you
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For the funcion has an absolute maximum. Now, apply the Maximum Modulus Principle. Fernando Revilla
If I using the maximum modulus principle, then i'll get |f(z)|<=|f(i)| for all z. But how could I find all the analytic funtions in |z|<3? Thank you
The function must be constant in . As there is only one function satisfyng the given hypothesis: .
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