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