Let be analytic on the unit disk, and assume that
1. for all and
2. .
Then and .
If either for some or if , then is a rotation, i.e., for some complex constant with .
Let be analytic on the unit disk, and assume that
1. for all and
2. .
Then and .
If either for some or if , then is a rotation, i.e., for some complex constant with .
Weisstein, Eric W. "Schwarz's Lemma." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchwarzsLemma.html