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.
We characterize all generalized lowpass filters and multiresolution analysis(MRA) Parseval frame wavelets in with matrix dilations of the form , where A is an arbitrary expanding matrix with integer coefficients, such that
. 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 and give an example to prove our theory.