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Show that there is no holomorphic fuction $f$ in the unit disc $D$ that extends continuously to boundary of $D$ such that $f(z)=\frac{1}{z} ~for~ z\in \partial( D) $.

I tried to apply maximum principle but I couln't find the way to prove it.

Help me please.

I just update the full statement and I think it probably assume it is not constant fuction.

Thank you.

  • 6
    The constant function $f(z)=0$ is holomorphic on the unit disk and extends continuously to the boundary of the disk. Are you sure you haven't misunderstood or misquoted the exercise?2012-10-10
  • 0
    I think the word "non-constant" may be missing in the OP.2012-10-10
  • 6
    The non-constant function $f(z)=z$ is holomorphic on the unit disk and extends continuously to the boundary of the disk.=2012-10-10
  • 1
    Could the upvoters explain how they understand the question?2012-10-10

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