The Characterization of Parseval Frame Wavelets

In this paper,we characterize all generalized low pass filters and MRA Parseval frame wavelets in L 2 (R n ) 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.We study the pseudo-scaling functions,generalized low pass filters and MRA Parseval frame wavelets and give some important characterizations about them.Furthermore,we give a characterization of the semiorthogonal MRA Parseval frame wavelets and provide several examples to verify our results.