Wavelet frames with irregular matrix dilations and their stability

Let psi is an element of L-2(R-n), B and A(j) (j is an element of Z) be real nonsingular n x n matrices, lambda(k) (k is an element of Z(n)) be real numbers. In this paper we present a sufficient condition for the system {\et A(j\\)(2)psi(A(j)x - Blambda(k)): j is an element of Z, k is an element of Z(n)} to be a frame for L-2(R-n). This sufficient condition also shows the stability of the system with respect to the perturbation of matrix dilation parameters {A(j)}(jis an element ofZ) and the perturbation of translation parameters {lambda(k)}(kis an element ofZn). (C) 2004 Elsevier Inc. All rights reserved.