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Journal of Mathematics
Volume 2013, Article ID 254694, 7 pages
Research Article

Convergence and Characterization of Wavelets Associated with Dilation Matrix in Variable Spaces

Department of Mathematics, Research and Post Graduate Studies, M. M. H. College, Model Town, Ghaziabad, Uttar Pradesh 20/001, India

Received 11 November 2012; Revised 17 January 2013; Accepted 18 January 2013

Academic Editor: Ding-Xuan Zhou

Copyright © 2013 Devendra Kumar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the convergence of wavelet expansions associated with dilation matrix in the variable spaces using the approximate identity. Also, we obtain conditions for the wavelet characterizations of with respect to norm estimates. Moreover, the results of Izuki (2008) and Kumar (2009) have been extended.