Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 492585, 17 pages
doi:10.1155/2009/492585
Research Article

MRA Parseval Frame Wavelets and Their Multipliers in L2(Rn)

Wu Guochang,1 Yang Xiaohui,2 and Liu Zhanwei3

1College of Information, Henan University of Finance and Economics, Zhengzhou 450002, China
2Institute of Applied Mathematics, College of Mathematics and Information Sciences, Henan University, Kaifeng 475004, China
3School of Information Engineering, Zhengzhou University, Zhengzhou 450001, China

Received 15 December 2008; Accepted 29 June 2009

Academic Editor: Victoria Vampa

Copyright © 2009 Wu Guochang et al. 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 characterize all generalized lowpass filters and multiresolution analysis(MRA) Parseval frame wavelets in L2(Rn) with matrix dilations of the form (Df)(x)=2f(Ax), where A is an arbitrary expanding n×n matrix with integer coefficients, such that |det⁡A|=2. At first, we study the pseudo-scaling functions, generalized lowpass filters, and multiresolution analysis (MRA) Parseval frame wavelets and give some important characterizations about them. Then, we describe the multiplier classes associated with Parseval frame wavelets in L2(Rn) and give an example to prove our theory.