Factorizations of analytic self-maps of the upper half-plane
Complex Variables
2012-05-08 v1
Abstract
We extend a factorization due to Krein to arbitrary analytic functions from the upper half-plane to itself. The factorization represents every such function as a product of fractional linear factors times a function which, generally, has fewer zeros and singularities than the original one. The result is used to construct functions with given zeros and poles on the real line.
Keywords
Cite
@article{arxiv.1205.1067,
title = {Factorizations of analytic self-maps of the upper half-plane},
author = {Hari Bercovici and Dan Timotin},
journal= {arXiv preprint arXiv:1205.1067},
year = {2012}
}