International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 67, Pages 3695-3702
doi:10.1155/S0161171204312457
Infinite matrices, wavelet coefficients and frames
1Department of Mathematics, National Institute of Technology, Srinagar, Kashmir 190006, Jammu and Kashmir, India
2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, Uttar Pradesh, India
3Department of Mathematics, Faculty of Science, P.O. Box 80203, King Abdul Aziz University, Jeddah, Saudi Arabia
Received 2 December 2003
Copyright © 2004 N. A. Sheikh and M. Mursaleen. 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.
Abstract
We study the action of A on f∈L2(ℝ) and on its wavelet coefficients, where A=(almjk)lmjk is a double infinite matrix. We find the frame condition for A-transform of f∈L2(ℝ) whose wavelet series expansion is known.