Characterization of Generators for Multiresolution Analyses with Composite Dilations

الملخص EN

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.