ComplexAnalysis2010jan - number A such that | A |> sup z...

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Complex Part 1. Show that the function f ( z ) = 1 /z has no a holomorphic anti- derivative on { < 1 < | z | < 2 } . 2. Suppose that f is an entire function and f 2 is a holomorphic polynomial. Show that f is also a holomorphic polynomial. 3. Suppose that a function f is meromorphic on the unit disk D and continuous in a neighborhood of its boundary D . Show that for any
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Unformatted text preview: number A such that | A | > sup z ∈ ∂ D | f ( z ) the number of zeros of the function f-A is equal to the number of poles of f in D . 4. Suppose that f and g are entire functions such that f ◦ g ( x ) = x when x ∈ R . Show that f and g are linear functions. 1...
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