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

We characterize all generalized lowpass filters and multiresolution analysis (MRA) Parseval frame wavelets in L-2(R-n) with matrix dilations of the form (Df)(x) = root 2f (Ax), where A is an arbitrary expanding n x n matrix with integer coefficients, such that vertical bar det A vertical bar = 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 L-2(R-n) and give an example to prove our theory. Copyright (C) 2009 Wu Guochang et al.