Characterization of Generators for Multiresolution Analyses with Composite Dilations - Yuan Zhu; Wenjun Gao; Dengfeng Li (Abstract and Applied Analysis)
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.