Characterization of Generators for Multiresolution Analyses with Composite Dilations

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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Main Authors: Yuan Zhu, Wenjun Gao, Dengfeng Li
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2011/850850
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spelling 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 AT yuanzhu characterizationofgeneratorsformultiresolutionanalyseswithcompositedilations
AT wenjungao characterizationofgeneratorsformultiresolutionanalyseswithcompositedilations
AT dengfengli characterizationofgeneratorsformultiresolutionanalyseswithcompositedilations
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