Biorthogonality and reproducing property
Integral operators involving the Szego, the Bergman and the Cauchy kernels are known to have the reproducing property, i.e. all of them reproduce holomorphic functions. Both the Szego and the Bergman kernels have series representations in terms of orthonormal basis. In this paper we derive the Cauch...
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| Main Authors: | , , |
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| Format: | Monograph |
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Jabatan Matematik, Universiti Teknologi Malaysia
1995
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/3869/ |
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| Institution: | Universiti Teknologi Malaysia |
| Summary: | Integral operators involving the Szego, the Bergman and the Cauchy kernels are known to have the reproducing property, i.e. all of them reproduce holomorphic functions. Both the Szego and the Bergman kernels have series representations in terms of orthonormal basis. In this paper we derive the Cauchy kernel by means of biorthogonality. The ideas involved are then applied to construct a non-Hermitian kernel admitting reproducing property for a space associated with the Bergman kernel. |
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