On the Dual Frame Induced by an Invertible Frame Multiplier

摘要

Recently it has been established that given an invertible framernmultiplier with semi-normalized symbol, a specific dual of any of the two in-rnvolved frames can be determined by the inversion process. The inverse can bernrepresented as a multiplier with the reciprocal symbol, this particular dualrnof one of the given frames, and any dual of the other frame. The specificrndual is the only one having this property among all Bessel sequences. Inrnthis manuscript we extend the results showing that the specific dual with thernabove mentioned property is unique among all possible sequences. Further-rnmore, the symbol is allowed to be not necessarily semi-normalized. Finallyrnwe characterize cases when the canonical dual frame and the new specificrndual frame coincide.