| A Note on Shift-Invariant Spaces Admitting a Single Generator |
| Received:February 21, 2009 Revised:April 26, 2010 |
| Key Words:
shift-invariant spaces sampling Riesz bases.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10871012) and the Natural Science Foundation of Beijing (Grant No.1082003). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.01.014 |
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