Stability and linear independence associated with wavelet decompositions
Rong Qing Jia, Jianzhong Wang · Proceedings of the American Mathematical Society · 1993
Wavelet decompositions are based on basis functions satisfying refinement equations. The stability, linear independence, and orthogonality of the integer translates of basis functions play an essential role in the study of wavelets. In this paper we characterize these properties in terms of the mask sequence in the refinement equation that the basis function satisfies.