| 李云章,廉巧芳.主平移不变子空间的平移整采样[J].数学年刊A辑,2009,30(2):189~200 |
| 主平移不变子空间的平移整采样 |
| Translated Integer Sampling in Principal Shift-Invariant Subspaces |
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| DOI： |
| 中文关键词: 标架 平移整采样 主平移不变子空间 |
| 英文关键词:Frame, Translated integer sampling, Principal shift-invariant subspace |
| 基金项目:国家自然科学基金，北京市自然科学基金，北京市中青年骨干教师基金和教育部留学回国人员科研启动基金联合资助项目 |
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| 中文摘要: |
| 给出主平移不变子空间的一个平移整采样定理,其采样公式不仅在L2(R)收敛意义下成立,而且在适当的1周期集上一致收敛的意义下成立.此采样定理包含了经典的Shannon采样公式,Walter在1992年的采样定理以及由紧支函数生成的主平移不变子空间的采样.最后给出了大量例子说明定理应用的广泛性. |
| 英文摘要: |
| In this paper, a translated integer sampling theorem is established in principal
shift-invariant frame subspaces, which is formulated in both L2(R) and uniform convergence
on some suitable 1-periodic set. The theorem covers the classical Shannon sampling formula,
Walter’s sampling theorem in 1992 and sampling in principal shift-invariant frame subspaces
with compactly supported generators. Many examples are also provided to illustrate its
generality. |
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