English

A characterization of M\"obius transformations

Complex Variables 2014-10-23 v1

Abstract

We prove that the derivative θ\theta' of an inner function θ\theta is outer if and only if θ\theta is a M\"obius transformation. An alternative characterization involving a reverse Schwarz--Pick type estimate is also given.

Cite

@article{arxiv.1410.6024,
  title  = {A characterization of M\"obius transformations},
  author = {Konstantin M. Dyakonov},
  journal= {arXiv preprint arXiv:1410.6024},
  year   = {2014}
}

Comments

4 pages

R2 v1 2026-06-22T06:32:40.814Z