Explicit formulae for the wave kernels for the Laplacians \(\Delta_{\alpha\beta}\) in the Bergman ball \(B^ n, n\geq 1\) (Q1361044)
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scientific article; zbMATH DE number 1038399
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Explicit formulae for the wave kernels for the Laplacians \(\Delta_{\alpha\beta}\) in the Bergman ball \(B^ n, n\geq 1\) |
scientific article; zbMATH DE number 1038399 |
Statements
Explicit formulae for the wave kernels for the Laplacians \(\Delta_{\alpha\beta}\) in the Bergman ball \(B^ n, n\geq 1\) (English)
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3 February 1998
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The authors establish explicit formulae for the kernels of the wave equation defined by the perturbed Bergman Laplacians on the unit ball of \(\mathbb{C}^n\). They then use analytic continuation arguments to give explicit formulae for the kernels of the wave equation defined by a two parameter family of Laplacians on \(\mathbb{C}^n\) which are natural deformations of the Fubini-Study Laplacian on projective space viewed as the dual space of the Bergman ball.
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Bergman ball
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hypergeometric functions
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Laplacian
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wave equation
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