- #1
arthurhenry
- 43
- 0
There does not exist a non-constant analytic function in the unit circle which is real valued on the unit circle.
I am not able to see why. I am trying to apply Louisville's Theorem, or maybe Open Mapping Th., but I fail.
Is there a way of extending this function so that it entire? and even then...why should it be bounded?
Thank you
I am not able to see why. I am trying to apply Louisville's Theorem, or maybe Open Mapping Th., but I fail.
Is there a way of extending this function so that it entire? and even then...why should it be bounded?
Thank you