|
Organizers |
Convergence of the continuous wavelet transforms on the entire Lebesgue set of Lp functions
by
Ravshan Ashurov
Institute of Advanced Technology (ITMA), University of Putra Malaysia
Coauthors: none
Under the minimal conditions on wavelets convergence almost-everywhere of wavelet transforms 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 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.
AMS 2000 Mathematics Subject
Classifications :
Primary 42C15; Secondary 40A30.
Key words: Continuous wavelet transforms,
Convergence, Lebesgue set.
Date received: January 14, 2010
Copyright © 2010 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cazv-17.