Characterization of Generators for Multiresolution Analyses with Composite Dilations
This paper introduces multiresolution analyses with composite dilations (AB-MRAs) and addresses frame multiresolution analyses with composite dilations in the setting of reducing subspaces of L2(ℝn) (AB-RMRAs). We prove that an AB-MRA can induce an AB-RMRA on a given reducing subspace L2(S)∨. For a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/850850 |
| Summary: | This paper introduces multiresolution analyses with composite dilations (AB-MRAs) and addresses frame multiresolution analyses with composite dilations in the setting
of reducing subspaces of L2(ℝn) (AB-RMRAs). We prove that an AB-MRA can induce an AB-RMRA on a given reducing subspace L2(S)∨. For a general expansive matrix, we obtain
the characterizations for a scaling function to generate an AB-RMRA, and the main theorems
generalize the classical results. Finally, some examples are provided to illustrate the general
theory. |
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| ISSN: | 1085-3375 1687-0409 |