The zeros of the Bergman kernel for some Reinhardt domains (Q340941)
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scientific article; zbMATH DE number 6653043
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The zeros of the Bergman kernel for some Reinhardt domains |
scientific article; zbMATH DE number 6653043 |
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The zeros of the Bergman kernel for some Reinhardt domains (English)
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15 November 2016
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Bergman kernel
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Reinhardt domain
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Lu Qi-Keng domain
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Consider the Reinhardt domain NEWLINE\[NEWLINE D_n=\Big\{(\zeta,z_1,\dots,z_n)\in\mathbb C^{n+1}:|\zeta|^2<\prod_{j=1}^n(1-|z_j|^2)\Big\}. NEWLINE\]NEWLINE The author obtains an explicit closed form of the Bergman kernel of the domain \(D_n\). As an application, he shows that the Bergman kernel of the domain \(D_n\) has zeros if and only if \(n\geq 3\).
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