Recent content by iamqsqsqs

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    Proving f is Constant: Entire Function with |f(z)|>1/(1+|z|) for all z in C

    If f is an entire function such that |f(z)|>1/(1+|z|) for all z in C. How can we show that f is a constant function
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    Holomorphic function on the unit disc

    How can we vigorously prove that? I am thinking of construct a function g such that g(1/n) = g(-1/n) = 1/n^2 and consider f/g to do it. However I am stuck and cannot go on
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    Holomorphic function on the unit disc

    Does there exist a holomorphic function f(z) on the unit disc and satisfies f(1/n) = f(-1/n) = 1/n^3 for every n in N?
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    Biholomorphic Mapping: Proving f(z) = z for All z in Ω?

    Suppose f is a biholomorphic mapping from Ω to Ω, if f(a) = a and f'(a) = 1 for some a in Ω, can we prove that f(z) = z for all z in Ω?
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    Find Entire Functions with |f(z)|=1 for all |z|=1: Proving Vigorously

    Difficult with this problem. Find all entire functions f such that |f(z)| = 1 for all z with |z| = 1. Are there any vigorous proofs?
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    Is f(x) Holomorphic if f(x)^2 and f(x)^3 Are?

    just figure out how to do it. just divide them and prove that the singularities must be isolated. otherwise f(z) will be constantly 0.
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    Is f(x) Holomorphic if f(x)^2 and f(x)^3 Are?

    If we know f(x)^2 and f(x)^3 are both holomorphic, can we say that f(x) itself is also holomorphic? And how to prove that?
    • iamqsqsqs
    • Thread
    • Analysis Complex Complex analysis
    • Replies: 3
    • Forum: Calculus
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