A Note on Shift-Invariant Spaces Admitting a Single Generator
Received:February 21, 2009  Revised:April 26, 2010
Key Word: shift-invariant spaces   sampling   Riesz bases.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10871012) and the Natural Science Foundation of Beijing (Grant No.1082003).
Author NameAffiliation
Jun Jian ZHAO Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, P. R. China
College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China 
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      In 2005, Garcia, Perez-Villala and Portal gave the regular and irregular sampling formulas in shift invariant space $V_\varphi$ via a linear operator $T$ between $L^2(0, 1)$ and $L^2(R)$. In this paper, in terms of bases for $L^2(0,\,\alpha)$, two sampling theorems for $\alpha{\mathbb{Z}}$-shift invariant spaces with a single generator are obtained.
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