Abstract
Optimal frame bounds play a key role in many applications of frame theory, such as filter banks. In this paper, we study the relation between the bounds of a frame and its alternate dual and then present some approach to construct a family of Parseval frames. Also, we survey some problems on duals of fusion frames. In particular, we discuss on some essential differences between duals of ordinary frames and fusion frames. Finally, we characterize duals of some fusion frames.
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