schwarz lemma
The Schwarz lemma is a theorem in complex analysis that relates the behavior of a holomorphic function within a disc to its maximum modulus on the boundary of that disc. It states that if a holomorphic function is bounded by 1 inside a disc centered at the origin, then its derivative at the origin is less than or equal to 1, and furthermore, this maximum modulus is achieved at any point inside the disc if and only if the function is constant.
Requires login.
Related Concepts (1)
Similar Concepts
- arnold-liouville theorem
- black and white thinking
- black holes
- black-and-white logic
- black-and-white reasoning
- black-and-white thinking
- black-or-white fallacy
- conjugacy theorem
- noether's theorem
- red-black tree
- red-black trees
- rolle's theorem
- schwarz reflection principle
- schwarzschild radius
- theorem proving