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Feb 27, 2013 at 2:11 comment added Alexandre Eremenko @Wolfgang: You modified your question (sorry I did not see it in time) and now I modified my answer.
Feb 27, 2013 at 2:10 history edited Alexandre Eremenko CC BY-SA 3.0
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Feb 26, 2013 at 9:04 comment added Wolfgang @ Alexandre: I don't get your point. I did modify my question (after Aaron's comment, already before you posted your answer) by making it clear that the roots should of course all be different, otherwise it becomes trivial. Moreover, if the polynomial has only (distinct) real roots, Ω is necessarily the real line, which is symmetric w.r.t. itself, thus excluded.
Feb 26, 2013 at 1:56 history answered Alexandre Eremenko CC BY-SA 3.0