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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 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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Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:850850
DOI: 10.1155/2011/850850
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