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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 20, Pages 3237-3245
http://dx.doi.org/10.1155/IJMMS.2005.3237

Wavelet-type frames and wavelet-type bases

Department of Mathematics, Imam Hossein University, P.O. Box 16895-198, Tehran, Iran

Received 13 January 2005; Revised 17 September 2005

Copyright © 2005 Hindawi Publishing Corporation. 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

The concepts of basis and frame are studied in the classical literature of functional analysis, Fourier analysis, and wavelet theory in a wide range. In this paper, we consider an operator-theoretic approach to discrete frame theory on a separable Hilbert space. For this purpose, we define a special type of frames and bases, called wavelet-type frames and wavelet-type bases, obtained by acting with a family of bounded linear operators on some vectors, and then investigate the elementary properties of these concepts.