主平移不变子空间的平移整采样

Translated Integer Sampling in Principal Shift-Invariant Subspaces

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L^2(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.

In this paper, a translated integer sampling theorem is established in principal shift-invariant frame subspaees, which is formulated in both L^2（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.