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Journal article
Stable polynomials and admissible numerators in product domains
The Bulletin of the London Mathematical Society, v 57(2), pp 377-394
01 Feb 2025
Abstract
Given a polynomial p$p$ with no zeros in the polydisk, or equivalently the poly-upper half-plane, we study the problem of determining the ideal of polynomials q$q$ with the property that the rational function q/p$q/p$ is bounded near a boundary zero of p$p$. We give a complete description of this ideal of numerators in the case where the zero set of p$p$ is smooth and satisfies a nondegeneracy condition. We also give a description of the ideal in terms of an integral closure when p$p$ has an isolated zero on the distinguished boundary. Constructions of multivariate stable polynomials are presented to illustrate sharpness of our results and necessity of our assumptions.
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Details
- Title
- Stable polynomials and admissible numerators in product domains
- Creators
- Kelly Bickel - Bucknell UniversityGreg Knese - Washington University in St. LouisJames Eldred Pascoe - Drexel University, MathematicsAlan Sola - Stockholm University
- Publication Details
- The Bulletin of the London Mathematical Society, v 57(2), pp 377-394
- Publisher
- Wiley
- Number of pages
- 18
- Grant note
- DMS-2000088; DMS-2247702; DMS-2319010 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001374102800001
- Scopus ID
- 2-s2.0-85211117546
- Other Identifier
- 991022006297004721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics