MRA Parseval Frame Wavelets and Their Multipliers inL2(Rn)

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, andmultiresolution analysis (MRA) Parseval frame wavelets and give some important characterizationsabout them. Then, we describe the multiplier classes associated with Parseval framewavelets in L2(Rn) and give an example to prove our theory