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Math Help - Complex analysis

  1. #1
    Junior Member
    Joined
    Apr 2010
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    58

    Complex analysis

    Help me please.
    Problem:
    1)Let f be an analityc function on the unit disk : D=\left \{ \left | z \right |<1 \right \} and f^2 - polynom in domain D.
    Is f analityc function in D?
    2)Let f be an entire function and f^2 polynom.
    Is  f polynom ?

    Thanks a lot.
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  2. #2
    Senior Member
    Joined
    Mar 2010
    From
    Beijing, China
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    Re: Complex analysis

    2) if f is analytic but not a polynomial, \infty is an essential singular point of f, so it is also an essential singular point of f^2, which contradicts the fact that f^2 is a polynomial.
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