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 multiresol
Translation and Dilation Invariance in Orthogonal Wavelets
โ Scribed by Gilbert G. Walter
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 331 KB
- Volume
- 1
- Category
- Article
- ISSN
- 1063-5203
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โฆ Synopsis
A multiresolution analysis for an orthogonal family of wavelets is usually not translation invariant. A concept of weak translation invariance is introduced and shown to hold for a class of Meyer wavelets and in fact characterizes this class. Other operators such as dilation, differentiation, and convolution are shown to have similar invariance properties for the same class. (s) 1944 Academic Press. Inc
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In a recent paper the creation operator of the quantum harmonic oscillator (its counterpart, the annihilation one as well) is characterized through its (spatial) translational invariance property. Here we step up with replacing the operator theoretic reasoning of [5] by an orthogonal polynomial env