A NOTE ON FINITE DUAL FRAME PAIRS

The purpose of this note is to extend certain key results in frame theory from the setting of tight frames to dual pairs of frames. We provide various characterizations of dual frame pairs {en}(n=1)(N), {f(n)}(n=1)(N) for a d-dimensional Hilbert space K-d. Based on this we characterize those scalar sequences {alpha(n)}(n=1)(N) for which there exist dual pairs of frames {e(n)}(n=1)(N), {f(n)}(n=1)(N) for K-d such that alpha(n) = < e(n), f(n)>. This generalizes the well-known fundamental inequality of tight frames.