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Mathematics > Functional Analysis

arXiv:math/0002127 (math)
[Submitted on 15 Feb 2000]

Title:Wavelets with the Translation Invariance Property of Order N

Authors:Sharon Schaffer (Colorado), Eric Weber (Texas A&M)
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Abstract: All wavelets can be associated to a multiresolution like structure, i.e. an incr easing sequence of subspaces of L^2(R). We consider the interaction of a wavel et and the translation operator in terms of which of the subspaces in this multi resolution like structure are invariant under the translation operator. This ac tion 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 di lation factors.
Comments: 17 pages; AMS-Latex
Subjects: Functional Analysis (math.FA)
MSC classes: 47A15; 46N99
Cite as: arXiv:math/0002127 [math.FA]
  (or arXiv:math/0002127v1 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.math/0002127

Submission history

From: Eric Weber [view email]
[v1] Tue, 15 Feb 2000 21:59:06 UTC (11 KB)
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