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| Content Provider | Springer Nature Link |
|---|---|
| Author | Blanchard, Jeffrey D. |
| Copyright Year | 2009 |
| Abstract | A composite dilation wavelet is a collection of functions generating an orthonormal basis for L 2(ℝ n ) under the actions of translations from a full rank lattice and dilations by products of elements of non-commuting groups A and B. A minimally supported frequency composite dilation wavelet has generating functions whose Fourier transforms are characteristic functions of a lattice tiling set. In this paper, we study the case where A is the group of integer powers of some expanding matrix while B is a finite subgroup of the invertible n×n matrices. This paper establishes that with any finite group B together with almost any full rank lattice, one can generate a minimally supported frequency composite dilation wavelet system. The paper proceeds by demonstrating the ability to find such minimally supported frequency composite dilation wavelets with a single generator. |
| Ending Page | 815 |
| Page Count | 20 |
| Starting Page | 796 |
| File Format | |
| ISSN | 10695869 |
| e-ISSN | 15315851 |
| Journal | Journal of Fourier Analysis and Applications |
| Issue Number | 6 |
| Volume Number | 15 |
| Language | English |
| Publisher | SP Birkhäuser Verlag Boston |
| Publisher Date | 2009-07-07 |
| Publisher Place | Boston |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Coxeter groups Reflection groups Reflection and Coxeter groups Signal, Image and Speech Processing Wavelet sets Wavelets and other special systems Abstract Harmonic Analysis Wavelets Mathematical Methods in Physics Reflection groups, reflection geometries Fourier Analysis Minimally supported frequency Composite dilation wavelets Approximations and Expansions Multiwavelets General harmonic expansions, frames Affine systems Partial Differential Equations |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Analysis |
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