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Abstract and Applied Analysis
Volume 2012, Article ID 746823, 14 pages
http://dx.doi.org/10.1155/2012/746823
Research Article

Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ

1Department of Mathematics, Shantou University, Guangdong, Shantou 515063, China
2Department of Mathematics, Hanshan Normal University, Guangdong, Chaozhou 521041, China

Received 10 March 2012; Accepted 19 May 2012

Academic Editor: Sergey V. Zelik

Copyright © 2012 D. H. Yuan et al. 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

We consider the multigenerator system , for and , , where the parameters are not necessary the same. With the help of frame theory, we provide some sufficient or necessary conditions for the system to be a frame for . Moreover, we present some characterizations for this system to be a Parseval frame.