基数正弦级数:过采样和不存在性

2015 International Conference on Sampling Theory and Applications (SampTA) Pub Date : 2015-05-25 DOI:10.1109/SAMPTA.2015.7148842

B. A. Bailey, W. Madych

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引用次数: 1

摘要

给出了样品f(n)、n = 0、±1、±2、…，整个函数f(z)的指数型小于π，这意味着相应的基数正弦级数收敛。这些条件是可能的同类条件中限制最少的。进一步，给出了一个π型指数函数f(z)在实轴上有界且其对应的基数正弦级数不收敛的例子。

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Cardinal sine series: Oversampling and non-existence

Growth conditions are given on the samples f(n), n = 0, ±1, ±2, ..., of an entire function f(z) of exponential type less than π that imply that the corresponding cardinal sine series converges. These conditions are the least restrictive of their kind that are possible. Furthermore, an example is provided of an entire function f(z) of exponential type π that is bounded on the real axis and whose corresponding cardinal sine series fails to converge.

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2015 International Conference on Sampling Theory and Applications (SampTA)

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