In this note, we solve the dynamical sampling problem for a class of shift-preserving operators $L:V\to V$ acting on a finitely generated shift-invariant space V. We find conditions on L and a finite set of functions of V so that the iterations of the operator L on the functions produce a frame generator set of V. This means that the integer translations of the generators form a frame of V.

中文翻译：

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保持班次的动态采样

在本说明中，我们解决了一类移位保持算子的动态采样问题 $\mathrm{大号}：V\to V$作用在有限生成平移不变空间V。我们找到L的条件和V的有限函数集，以便运算符L在函数上的迭代产生V的帧生成器集。这意味着生成器的整数平移形成V的框架。