No abstract

Abstract. All wavelets can be associated to a multiresolution-like structure, i.e. an increasing sequence of subspaces of L 2 (R). We consider the interaction of a wavelet and the shift operator in terms of which of the subspaces in this multiresolution-like structure are invariant under the shift operator. This action defines the notion of the shift invariance property of order n. In this paper we show that wavelets of all levels of shift invariance exist, first for the classic case of dilation by 2, and then for arbitrary integral dilation factors.