On frame wavelets associated with frame multiresolution analysis

Abstract

We present some necessary and sufficient conditions for a frame multiresolution analysis (FMRA) to admit a Frame wavelet whose dyadic dilations and integer translates generate a frame for L-2(R) and propose a construction of a wavelet, if it exists, which reduces to the classical orthonormal wavelet in the case of orthonormal multiresolution analysis. We also show that there always exists a frame for the detail space W-0 of a Frame MRA consisting of the integer translates of two functions and give an explicit construction of them. (C) 2001 Academic Press.