New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous Frames. (9th June 2013)

• Record Type: Journal Article
• Authors: Xiang, Zhong-Qi
• Other Names: Leandre Remi Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2013(2013)
• Publication Date: 2013-06-09
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2013/298982
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : 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 operatorL . 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.