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Convergence of the continuous wavelet transforms on the entire Lebesgue set of Lp functions

Ashurov, Ravshan (2010) Convergence of the continuous wavelet transforms on the entire Lebesgue set of Lp functions. In: 6th International Conference: 2010-Dynamical Systems and Application, 10-14 July 2010, Antalya,Turkey.

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Abstract

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.

Item Type:Conference or Workshop Item (Paper)
Keyword:Continuous wavelet transforms; Convergence; Lebesgue set
Subject:Wavelets (Mathematics)
Subject:Convergence
Subject:Measure theory
Faculty or Institute:Institute of Advanced Technology
ID Code:17985
Deposited By: kmportal
Deposited On:08 Sep 2011 16:56
Last Modified:17 Nov 2014 10:20

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