On frames, dual frames, and the duality principle

Diana T. Stoeva

Frames in Hilbert spaces generalize orthonormal bases and allow stable representation of all the elements of the space via a given frame and its dual frame. Frames are not only interesting from theoretical point of view, but play significant role in signal and image processing, which leads to many applications in informatics, engineering, medicine, and many other fields. In this paper we give a short survey on the theory for frames in Hilbert spaces, with focus on the duality principle and related open problems. It is the author's hope that this presentation will contribute to the solution of some of the deep problems that remain open despite the intensive development of frame theory during the last decade.