On a certain generalization of the Carathéodory-Julia-Wolff theorem (Q550442)
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scientific article; zbMATH DE number 5919206
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a certain generalization of the Carathéodory-Julia-Wolff theorem |
scientific article; zbMATH DE number 5919206 |
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On a certain generalization of the Carathéodory-Julia-Wolff theorem (English)
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11 July 2011
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Let \(s\) be a holomorphic selfmap of the unit disk \(\mathbb D\) and let \(b\) be a finite Blaschke product of degree \(k\). The author presents necessary and sufficient conditions for \(s-b\) to have exactly \(k\) zeros inside \(\mathbb D\). A Carathéodory-Julia-Wolff type theorem for meromorphic functions is obtained as a corollary. We refer the reader also to the author's follow-up paper [Integral Equations Oper. Theory 69, No. 2, 203--215 (2011; Zbl 1211.30006)].
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analytic selfmaps of the disk
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Carathéodory-Wolff-Julia type theorem
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meromorphic functions in the disk
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Blaschke products
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