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Abstract
The main purpose of this paper is to establish a necessary condition and two sufficient conditions ensuring that the shift-invariant system is a frame for 
. As some applications, the results are used to obtain some known conclusions about wavelet frames and Gabor frames.
Received: 2010-04-04
Revised: 2010-12-24
Published Online: 2011-December
Published in Print: 2011-December
de Gruyter 2011
