The generalized sampling theorem for transforms of not necessarily square integrable functions
It is known that the generalized sampling theorem is valid for certain finite limit integral transforms of square integrable functions. In this note, we will extend the validity of the theorem to include transforms of absolutely integrable functions associated with differentiable kernels. In the pro...
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000369 |
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| _version_ | 1850166446397587456 |
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| author | A. J. Jerri |
| author_facet | A. J. Jerri |
| author_sort | A. J. Jerri |
| collection | DOAJ |
| description | It is known that the generalized sampling theorem is valid for certain finite limit integral transforms of square integrable functions. In this note, we will extend the validity of the theorem to include transforms of absolutely integrable functions associated with differentiable kernels. In the proof, we will use the Hölder inequality and a known theorem concerning the uniform convergence of the orthogonal series to the differentiable kernel of the particular integral transform. |
| format | Article |
| id | doaj-art-d93fd9bb2ae1462a956ee90c5f81699f |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d93fd9bb2ae1462a956ee90c5f81699f2025-08-20T02:21:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018235535810.1155/S0161171285000369The generalized sampling theorem for transforms of not necessarily square integrable functionsA. J. Jerri0Department of Mathematics and Computer Science, Clarkson College of Technology, Potsdam 13676, N.Y., USAIt is known that the generalized sampling theorem is valid for certain finite limit integral transforms of square integrable functions. In this note, we will extend the validity of the theorem to include transforms of absolutely integrable functions associated with differentiable kernels. In the proof, we will use the Hölder inequality and a known theorem concerning the uniform convergence of the orthogonal series to the differentiable kernel of the particular integral transform.http://dx.doi.org/10.1155/S0161171285000369sampling theoremintegral transformsabsolutely integrable functions. |
| spellingShingle | A. J. Jerri The generalized sampling theorem for transforms of not necessarily square integrable functions International Journal of Mathematics and Mathematical Sciences sampling theorem integral transforms absolutely integrable functions. |
| title | The generalized sampling theorem for transforms of not necessarily square integrable functions |
| title_full | The generalized sampling theorem for transforms of not necessarily square integrable functions |
| title_fullStr | The generalized sampling theorem for transforms of not necessarily square integrable functions |
| title_full_unstemmed | The generalized sampling theorem for transforms of not necessarily square integrable functions |
| title_short | The generalized sampling theorem for transforms of not necessarily square integrable functions |
| title_sort | generalized sampling theorem for transforms of not necessarily square integrable functions |
| topic | sampling theorem integral transforms absolutely integrable functions. |
| url | http://dx.doi.org/10.1155/S0161171285000369 |
| work_keys_str_mv | AT ajjerri thegeneralizedsamplingtheoremfortransformsofnotnecessarilysquareintegrablefunctions AT ajjerri generalizedsamplingtheoremfortransformsofnotnecessarilysquareintegrablefunctions |