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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| Format: | Monograph |
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Jabatan Matematik, Universiti Teknologi Malaysia
1995
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| _version_ | 1825909458992103424 |
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| author | Murid, Ali H.M. Razali, Mohd. R.M Nashed, M.Z |
| author_facet | Murid, Ali H.M. Razali, Mohd. R.M Nashed, M.Z |
| author_sort | Murid, Ali H.M. |
| collection | ePrints |
| description | 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. |
| first_indexed | 2024-03-05T18:02:28Z |
| format | Monograph |
| id | utm.eprints-3869 |
| institution | Universiti Teknologi Malaysia - ePrints |
| last_indexed | 2024-03-05T18:02:28Z |
| publishDate | 1995 |
| publisher | Jabatan Matematik, Universiti Teknologi Malaysia |
| record_format | dspace |
| spelling | utm.eprints-38692007-06-29T03:16:27Z http://eprints.utm.my/3869/ Biorthogonality and reproducing property Murid, Ali H.M. Razali, Mohd. R.M Nashed, M.Z QA Mathematics 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. Jabatan Matematik, Universiti Teknologi Malaysia 1995 Monograph NonPeerReviewed Murid, Ali H.M. and Razali, Mohd. R.M and Nashed, M.Z (1995) Biorthogonality and reproducing property. Technical Report. Jabatan Matematik, Universiti Teknologi Malaysia. |
| spellingShingle | QA Mathematics Murid, Ali H.M. Razali, Mohd. R.M Nashed, M.Z Biorthogonality and reproducing property |
| title | Biorthogonality and reproducing property |
| title_full | Biorthogonality and reproducing property |
| title_fullStr | Biorthogonality and reproducing property |
| title_full_unstemmed | Biorthogonality and reproducing property |
| title_short | Biorthogonality and reproducing property |
| title_sort | biorthogonality and reproducing property |
| topic | QA Mathematics |
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