New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous Frames

Abstract EN

We give new characterizations of Riesz-type frames, on equivalent conditions for a continuous frame to be a Riesz-type frame and on equivalency relations between Riesz-type frames and continuous frames.

We characterize also the Riesz-type frames by using a bounded linear operator L.

Finally, we study the stability of alternate duals of continuous frames and we prove that if two continuous frames are close to each other, then we can find alternate duals of them which are close to each other.