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Math Help - analytic function

  1. #1
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    analytic function

    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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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    For z=i the funcion |f| has an absolute maximum. Now, apply the Maximum Modulus Principle.


    Fernando Revilla
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  3. #3
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    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
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    The function f must be constant in |z|<3 . As f(i)=-3i there is only one function satisfyng the given hypothesis: f(z)=-3i .
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