Characterization of Generators for Multiresolution Analyses with Composite Dilations

Yuan Zhu, Wenjun Gao, Dengfeng Li
2011 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 ofL2(ℝn)(AB-RMRAs). We prove that an AB-MRA can induce an AB-RMRA on a given reducing subspaceL2(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.
doi:10.1155/2011/850850 fatcat:zfkxhdws7fcb7kpd5xeg3f7shq