Frames of Translates and Examples of Generalized Frame Multiresolution Analyses

摘要

We introduce the concept of frames of translates and we characterize the countable families of vectors generating such frames. In this context we generalize the concept of the Grammian introduced by Ron and Shen. We apply this characterization to study Generalized frame MRAs of L~2(R). We also provide the characterization of frame multiwavelet sets associated with GFMRAs of L~2(R) and we present examples of GFMRAs.