On the pointwise convergence of the continuous wavelet transforms of Lp-functions
1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 organized by Universiti Malaysia Perlis (UniMAP) and co-organized by Universiti Sains Malaysia (USM) & Universiti Kebangsaan Malaysia (UKM), 2nd - 3rd June 2010 at Eastern & Oriental Hotel, Penang.
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Universiti Malaysia Perlis (UniMAP)
2010
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| Online Access: | http://dspace.unimap.edu.my/xmlui/handle/123456789/10262 |
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my.unimap-102622010-11-23T03:30:49Z On the pointwise convergence of the continuous wavelet transforms of Lp-functions Ashurov, Ravshan ashurovr@yahoo.com Continuous wavelet transforms Convergence Lebesgue set Regional Conference on Applied and Engineering Mathematics (RCAEM) 1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 organized by Universiti Malaysia Perlis (UniMAP) and co-organized by Universiti Sains Malaysia (USM) & Universiti Kebangsaan Malaysia (UKM), 2nd - 3rd June 2010 at Eastern & Oriental Hotel, Penang. Under the minimal conditions on wavelets convergence almost-everywhere of wavelet transforms of Lp-functions (p>1) 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 convergence. 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. We also prove that the same conditions on wavelets guarantee the Riemann localization principle in L1 for the wavelet transforms. 2010-11-23T03:30:49Z 2010-11-23T03:30:49Z 2010-06-02 Working Paper Vol.1(5), p.53-55 http://hdl.handle.net/123456789/10262 en Proceedings of the 1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 Universiti Malaysia Perlis (UniMAP) Institut Matematik Kejuruteraan |
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English |
| topic |
Continuous wavelet transforms Convergence Lebesgue set Regional Conference on Applied and Engineering Mathematics (RCAEM) |
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Continuous wavelet transforms Convergence Lebesgue set Regional Conference on Applied and Engineering Mathematics (RCAEM) Ashurov, Ravshan On the pointwise convergence of the continuous wavelet transforms of Lp-functions |
| description |
1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 organized by Universiti Malaysia Perlis (UniMAP) and co-organized by Universiti Sains Malaysia (USM) & Universiti Kebangsaan Malaysia (UKM), 2nd - 3rd June 2010 at Eastern & Oriental Hotel, Penang. |
| author2 |
ashurovr@yahoo.com |
| author_facet |
ashurovr@yahoo.com Ashurov, Ravshan |
| format |
Working Paper |
| author |
Ashurov, Ravshan |
| author_sort |
Ashurov, Ravshan |
| title |
On the pointwise convergence of the continuous wavelet transforms of Lp-functions |
| title_short |
On the pointwise convergence of the continuous wavelet transforms of Lp-functions |
| title_full |
On the pointwise convergence of the continuous wavelet transforms of Lp-functions |
| title_fullStr |
On the pointwise convergence of the continuous wavelet transforms of Lp-functions |
| title_full_unstemmed |
On the pointwise convergence of the continuous wavelet transforms of Lp-functions |
| title_sort |
on the pointwise convergence of the continuous wavelet transforms of lp-functions |
| publisher |
Universiti Malaysia Perlis (UniMAP) |
| publishDate |
2010 |
| url |
http://dspace.unimap.edu.my/xmlui/handle/123456789/10262 |
| _version_ |
1643789781375647744 |