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Math Help - bounded anlaytic function.

  1. #1
    Ant
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    bounded anlaytic function.

    Let f be analytic in the open disk D(z_{0},R). Let r< R\hat and \gamma_{r} be the anticlockwise oreinted circle of radius r centered at z_{0}.

    Let w \in tr \gamma_{r}.

    Does it follow that f(w) is bounded on tr \gamma_{r}?

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  2. #2
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    Re: bounded anlaytic function.

    what is "tr"?
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  3. #3
    Ant
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    Re: bounded anlaytic function.

    sory, it denotes the trace of \gamma_{r}. i.e. the image of the map/contour \gamma_{r}.
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  4. #4
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    Re: bounded anlaytic function.

    A circle is compact so any continuous function on it is bounded.
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