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Preprint
Stable polynomials and bounded rational functions in the unit ball
pp 1-33
24 Feb 2026
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.
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Details
- Title
- Stable polynomials and bounded rational functions in the unit ball
- Creators
- Greg Knese - Washington University in St. LouisJames Eldred Pascoe - Drexel UniversityAlan Sola - Stockholm University
- Publication Details
- pp 1-33
- Number of pages
- 33
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022163437304721