Orthonormal wavelets and shift invariant generalized multiresolution analyses |
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| Authors: | Sharon Schaffer Vestal Eric Weber |
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| Affiliation: | Department of Mathematics, University of Colorado, Boulder, Colorado 80309-0395 ; Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368 |
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| Abstract: | All wavelets can be associated to a multiresolution-like structure, i.e. an increasing sequence of subspaces of  . 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  . 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. |
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| Keywords: | Wavelet GMRA shift invariant space |
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