English

Linear Fractional Self-Maps of the Unit Ball in $\mathbb{C}^N$

Complex Variables 2023-10-03 v1

Abstract

Determining the range of complex maps plays a fundamental role in the study of several complex variables and operator theory. In particular, one is often interested in determining when a given holomorphic function is a self-map of the unit ball. In this paper, we discuss a class of maps in CN\mathbb{C}^N that generalize linear fractional maps. We then proceed to determine precisely when such a map is a self-map of the unit ball. In particular, we take a novel approach obtaining numerous new results about this class of maps along the way.

Keywords

Cite

@article{arxiv.2310.00787,
  title  = {Linear Fractional Self-Maps of the Unit Ball in $\mathbb{C}^N$},
  author = {Michael R. Pilla},
  journal= {arXiv preprint arXiv:2310.00787},
  year   = {2023}
}