Convergence of the continuous wavelet transforms on the entire Lebesgue set of Lp functions
Under the minimal conditions on wavelets convergence almost- everywhere of wavelet transform of Lp functions is well known. But this result is not completely satisfying for the reason, that we have no information about the exceptional set (of measure zero), where there is no convengence. In this pap...
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| Main Author: | |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/17985/1/ID%2017985.pdf http://psasir.upm.edu.my/id/eprint/17985/ |
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| Institution: | Universiti Putra Malaysia |
| Language: | English |
| Summary: | Under the minimal conditions on wavelets convergence almost- everywhere of wavelet transform of Lp functions is well known. But this result is not completely satisfying for the reason, that we have no information about the exceptional set (of measure zero), where there is no convengence. In this paper under the slightly stronger conditions on wavelets we prove convergence of wavelet transforms everywhere on the entire Lebesgue set of Lp functions. On the other hand, practically all the wavelets, like Haar and 'French hat' wavelets,used frequently in applications,satisfy our conditions. |
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