A new Morera-type theorem on the unit disk (Q2754810)
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scientific article; zbMATH DE number 1668433
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new Morera-type theorem on the unit disk |
scientific article; zbMATH DE number 1668433 |
Statements
4 November 2001
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Morera theorem
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Iwasawa decomposition
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A new Morera-type theorem on the unit disk (English)
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Let \(G\) be the group of conformal automorphisms of the complex unit disk \(D\) and let \(G=KAN\) be its Iwasawa decomposition. The author finds such a contour \(Q\subset D\) that the condition NEWLINE\[NEWLINE \int\limits_{\partial (gQ)}f(z) dz=0\quad \text{for all }g\in NA, NEWLINE\]NEWLINE together with some assumptions regarding the asymptotic behaviour of a continuous function \(f\) as \(z\to 1\), implies holomorphy of \(f\).
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