Representation of holomorphic function with minimum norm (Q2767897)
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scientific article; zbMATH DE number 1698735
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Representation of holomorphic function with minimum norm |
scientific article; zbMATH DE number 1698735 |
Statements
7 November 2002
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Bergman space
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diagonal map
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Hardy space
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minimum norm
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reproducing kernel
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Representation of holomorphic function with minimum norm (English)
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W. Rudin proved that the image of the Hardy space on the polydisc in \({\mathbb C}^2\) under the diagonal map is characterized by members of the Bergman space on the unit disc. C. Horowitz and D. M. Oberin obtained an analogous result for the Bergman space on the unit polydisc in \({\mathbb C}^n\). NEWLINENEWLINENEWLINEIn this paper the authors characterize the images of the Bergman space and the Hardy space on the unit ball in \({\mathbb C}^n\) under the diagonal map.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00006].
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