Stable polynomials and bounded rational functions in the unit ball
Complex Variables
2026-02-25 v1 Algebraic Geometry
Abstract
We study polynomials with no zeros on the unit ball in complex Euclidean space with a view toward characterizing when a rational function is bounded on the ball. We give a complete local description of such polynomials in two variables near a boundary zero. In higher dimensions, we give a partial characterization of a simple boundary zero. Several applications are given including boundedness of rational functions with boundary singularities and constructions of examples with prescribed local properties.
Cite
@article{arxiv.2602.21051,
title = {Stable polynomials and bounded rational functions in the unit ball},
author = {Greg Knese and James Eldred Pascoe and Alan Sola},
journal= {arXiv preprint arXiv:2602.21051},
year = {2026}
}