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Dieudonne criterion

  1. May 3, 2010 #1
    1. The problem statement, all variables and given/known data

    prove for the dieudonne criterion on univalent polynomials.
    polyn. of degree n is univalent in the open disk iff sum(k=1 --> n) a_k sin(kt)/sint z^(k-1)
    is not 0 in open unit disk, given 0 < t < pi/2


    2. Relevant equations
    hint: Polyn. univ iff [p(ze^it) - p(ze^-it)]/z(e^it - e^-it) =/= 0 in open unit disk


    3. The attempt at a solution
    all failed attempts. need a hint to begin, thank you all is appreciated.
     
  2. jcsd
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