Interview Question: Bounded and Entire Mean Constant

Sample Question #112 (mathematics – complex analysis)

Let f(x) be an entire function. Show that if f(x) is also bounded, then f(x) is a constant function.

(Comment: if you took a complex analysis course, you might be asked questions like this. I personally think whoever asks this kind of question is quite a sadist at heart.)

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One Response to Interview Question: Bounded and Entire Mean Constant

  1. Brett says:

    ANSWER
     
    This very interesting result is known as Liouville’s Theorem and has important applications in classical mechanics (but I know of no application in finance). The proof can be found here. 

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