Universal holomorphic and harmonic functions with additional properties (Q558279)
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scientific article; zbMATH DE number 2186355
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Universal holomorphic and harmonic functions with additional properties |
scientific article; zbMATH DE number 2186355 |
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Universal holomorphic and harmonic functions with additional properties (English)
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5 July 2005
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Based on the concept of so-called (total) omnipresence of operators, several results on the genericity of (translation-dilation) universal functions are proved. Mainly to have a unified approach to holomorphic and harmonic functions, in the first part operators on spaces of \(P\)-holomorphic functions are considered. The second part is devoted to holomorphic functions having lacunary power series structure and to holomorphic functions which are univalent in certain prescribed sets.
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\(P\)-holomorphic functions
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totally omnipresent operators
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universal functions
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lacunary holomorphic functions
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harmonic functions
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univalence
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residual set
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