English

On weighted compositions preserving the Carath\'eodory class

Complex Variables 2018-10-31 v2

Abstract

We characterize in various ways the weighted composition transformations which preserve the class P{\mathcal P} of normalized analytic functions in the disk with positive real part. We analyze the meaning of the criteria obtained for various special cases of symbols and identify the fixed points of such transformations.

Cite

@article{arxiv.1608.04577,
  title  = {On weighted compositions preserving the Carath\'eodory class},
  author = {Irina Arévalo and Rodrigo Hernández and María J. Martín and Dragan Vukotić},
  journal= {arXiv preprint arXiv:1608.04577},
  year   = {2018}
}

Comments

16 pages, 1 figure. A new comment and one minor correction were included in this version

R2 v1 2026-06-22T15:20:56.285Z