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Translation and Dilation Invariant Subspaces ofL2(R) and Multiresolution Analyses

✍ Scribed by R.A. Lorentz; W.R. Madych; A. Sahakian

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 192 KB
Volume: 5
Category: Article
ISSN: 1063-5203
DOI: 10.1006/acha.1998.0235

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✦ Synopsis

We characterize the closure of the union of the subspaces of a multiresolution analysis which does not necessarily enjoy the usual density property. One consequence of our development is that in many instances the density hypothesis is redundant. Another consequence is the fact that every multiresolution analysis can be complemented by another so that the orthogonal direct sum is dense in L 2 ‫.)ޒ(‬ ᭧ 1998 Academic Press One reason for our interest in this question is that its answer throws light on those properties of the scaling function which imply that ʜ j ‫ޚ√‬ V j is dense in L 2 ‫.)ޒ(‬ Indeed, it is generally known that the usual definitions of a multiresolution analysis found in,

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Two numerical characteristics for estimation of translation invariance of a multiresolution analysis (MRA) of L 2 (R) are proposed. These two characteristics are defined either through the scaling function or through the scaling symbol of the MRA. Some simple conditions under which both translation