Stable polynomials and bounded rational functions in the unit ball
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912923370127360 |
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| author | Knese, Greg Pascoe, James Eldred Sola, Alan |
| author_facet | Knese, Greg Pascoe, James Eldred Sola, Alan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21051 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stable polynomials and bounded rational functions in the unit ball Knese, Greg Pascoe, James Eldred Sola, Alan Complex Variables Algebraic Geometry 14H45, 32A08, 32B05 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. |
| title | Stable polynomials and bounded rational functions in the unit ball |
| topic | Complex Variables Algebraic Geometry 14H45, 32A08, 32B05 |
| url | https://arxiv.org/abs/2602.21051 |