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Characterization of Generators for Multiresolution Analyses with Composite Dilations

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  • Yuan Zhu
  • Wenjun Gao
  • Dengfeng Li

Abstract

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 ð ¿ 2 ( â„ ð ‘› ) (AB-RMRAs). We prove that an AB-MRA can induce an AB-RMRA on a given reducing subspace ð ¿ 2 ( 𠑆 ) ∨ . 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.

Suggested Citation

  • Yuan Zhu & Wenjun Gao & Dengfeng Li, 2011. "Characterization of Generators for Multiresolution Analyses with Composite Dilations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-13, March.
    • Handle: RePEc:hin:jnlaaa:850850
    DOI: 10.1155/2011/850850
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