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Advances in Mathematical Physics
Volume 2016 (2016), Article ID 3783456, 6 pages
http://dx.doi.org/10.1155/2016/3783456
Research Article

Tight --Frame and Its Novel Characterizations via Atomic Systems

School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China

Received 2 November 2015; Revised 5 January 2016; Accepted 6 January 2016

Academic Editor: Remi Léandre

Copyright © 2016 Yongdong Huang and Dingli Hua. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

-frame is a generalization of -frame. We generalize the tight -frame to --frame via atomic systems. In this paper, the definition of tight --frame is put forward; equivalent characterizations and necessary conditions of tight --frame are given. In particular, the necessary and sufficient condition for tight --frame being tight -frame is obtained. Finally, by means of methods and techniques of frame theory, several properties of tight --frame are given.