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Bounded polynomials and holomorphic mappings between convex subrings of \(^\ast\mathbb C\). (English) Zbl 1401.30055
Summary: Using convex subrings of \(^\ast\mathbb{C}\), a nonstandard extension of \(\mathbb{C}\), we define several kinds of complex bounded polynomials and we provide their associated analytic functions obtained by taking the quasistandard part.

MSC:
30G06 Non-Archimedean function theory
03H05 Nonstandard models in mathematics
26E35 Nonstandard analysis
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