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...
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doaj-577bf3801b7e40589a8b0dcbf722eb1c2020-11-24T23:59:00ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/850850850850Characterization of Generators for Multiresolution Analyses with Composite DilationsYuan Zhu0Wenjun Gao1Dengfeng Li2School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, ChinaBasic Department, Henan Quality and Engineering Vocational College, Pingdingshan 467000, ChinaSchool of Mathematics and Information Sciences, Henan University, Kaifeng 475001, ChinaThis 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.http://dx.doi.org/10.1155/2011/850850 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Yuan Zhu Wenjun Gao Dengfeng Li |
spellingShingle |
Yuan Zhu Wenjun Gao Dengfeng Li Characterization of Generators for Multiresolution Analyses with Composite Dilations Abstract and Applied Analysis |
author_facet |
Yuan Zhu Wenjun Gao Dengfeng Li |
author_sort |
Yuan Zhu |
title |
Characterization of Generators for Multiresolution Analyses with Composite Dilations |
title_short |
Characterization of Generators for Multiresolution Analyses with Composite Dilations |
title_full |
Characterization of Generators for Multiresolution Analyses with Composite Dilations |
title_fullStr |
Characterization of Generators for Multiresolution Analyses with Composite Dilations |
title_full_unstemmed |
Characterization of Generators for Multiresolution Analyses with Composite Dilations |
title_sort |
characterization of generators for multiresolution analyses with composite dilations |
publisher |
Hindawi Limited |
series |
Abstract and Applied Analysis |
issn |
1085-3375 1687-0409 |
publishDate |
2011-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2011/850850 |
work_keys_str_mv |
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1725448732432924672 |