Frame Potential of Dual Frames and Phase Retrievable Frames

This paper is concentrated on the frame potential of finite frames in n-dimensional Hilbert space H-n. More precisely, We define the relative frame potential of two sequences F and G in H-n, which is denoted by (FP) over tilde (F, G). For dual frames F and G in H-n, we show that G is canonical dual frame of F if and only (FP) over tilde (F, G) = n. A lower and upper bound for (FP) over tilde (F, G) is given, for the case that F and G are frames for H-n. Also, using the relative frame potential of the sub sequences of a given frame, some equivalent conditions for its phase retrievability and its norm retrievability, are presented.