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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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Bibliographic Details
Main Author: Ashurov, Ravshan
Other Authors: ashurovr@yahoo.com
Format: Working Paper
Language:English
Published: Universiti Malaysia Perlis (UniMAP) 2010
Subjects:
Continuous wavelet transforms
Convergence
Lebesgue set
Regional Conference on Applied and Engineering Mathematics (RCAEM)
Online Access:http://dspace.unimap.edu.my/xmlui/handle/123456789/10262
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spelling 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
institution Universiti Malaysia Perlis
building UniMAP Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Perlis
content_source UniMAP Library Digital Repository
url_provider http://dspace.unimap.edu.my/
language English
topic Continuous wavelet transforms
Convergence
Lebesgue set
Regional Conference on Applied and Engineering Mathematics (RCAEM)
spellingShingle 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
score 13.214268

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