Abstract In this paper, we study the sampling and average sampling problem in a quasi shift-invariant space where X is a discrete subset of and is a continuously differentiable positive definite function satisfying certain decay conditions. We show that any f belonging to can be uniquely and stably reconstructed from its samples as well as from its average samples provided sampling points are close enough. Further, iterative reconstruction algorithms for reconstruction of a function f belonging to from its samples as well as from its average samples are also provided.

中文翻译：

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准平移不变空间中的采样和平均采样

摘要 在本文中，我们研究了准平移不变空间中的采样和平均采样问题，其中 X 是满足一定衰减条件的连续可微正定函数的离散子集。我们表明，只要采样点足够接近，就可以从其样本及其平均样本中唯一且稳定地重建属于的任何 f。此外，还提供了用于从其样本及其平均样本重构属于函数 f 的迭代重构算法。