Algebraic and geometric aspects of rational $Γ$-inner functions Article Swipe

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Jim Agler , Zinaida A. Lykova , N. J. Young ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1502.04216

The set \[ Γ{\stackrel{\rm def}{=}} \{(z+w,zw):|z|\leq 1,|w|\leq 1\} \subset {\mathbb{C}}^2 \] has intriguing complex-geometric properties; it has a 3-parameter group of automorphisms, its distinguished boundary is a ruled surface homeomorphic to the Möbius band and it has a special subvariety which is the only complex geodesic that is invariant under all automorphisms. We exploit this geometry to develop an explicit and detailed structure theory for the rational maps from the unit disc to $Γ$ that map the boundary of the disc to the distinguished boundary of $Γ$.

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Mathematics Algebraic number Algebra over a field Pure mathematics Mathematical economics Mathematical analysis

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Type: preprint
Language: en
Landing Page: https://doi.org/10.48550/arxiv.1502.04216
OA Status: green
Cited By: 1
Related Works: 10
OpenAlex ID: https://openalex.org/W4394653203

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DOI: https://doi.org/10.48550/arxiv.1502.04216

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Title: Algebraic and geometric aspects of rational $Γ$-inner functions

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Type: preprint

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Language: en

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Publication year: 2015

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Publication date: 2015-02-14

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Authors: Jim Agler, Zinaida A. Lykova, N. J. Young

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Landing page: https://doi.org/10.48550/arxiv.1502.04216

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Concepts: Mathematics, Algebraic number, Algebra over a field, Pure mathematics, Mathematical economics, Mathematical analysis

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Cited by: 1

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