1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Complex analysis - Schwarz's Lemma

  1. Apr 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that M|[itex]\frac{f(z)-f(z_{0})}{M^2-\overline{f(z_{0})}f(z)}[/itex]|≤|[itex]\frac{z-z_{0}}{1-\overline{z_{0}}z}[/itex]|

    for all z, z[itex]_{0}[/itex] in {w:|w|<1|

    2. Relevant equations

    I think I will have to use Schwarz's Lemma: if f is analytic in disc |z|<1, f(0)=0, and |f(z)|≤1 for all z in the disc, then |f(z)|≤|z| , |z|<1

    3. The attempt at a solution

    This looks similar to Schwarz Pick Theorem (found online, don't completely understand..)

    but one of the steps they used was to fix z which would mean that f(z)=z so the equations would become M|[itex]\frac{z-f(z_{0})}{M^2-\overline{f(z_{0})}z}[/itex]|≤|[itex]\frac{f(z)-z_{0}}{1-\overline{z_{0}}f(z)}[/itex]| or M|[itex]\frac{z-f(z_{0})}{M^2-\overline{f(z_{0})}z}[/itex]|≤|[itex]\frac{z-z_{0}}{1-\overline{z_{0}}z}[/itex]| not sure how that would help though...
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted