Abstract:Four special subsets of the Schwartz algebra are defined (this algebra consists of all entire functions of exponential type and of polynomial growth on the real axis). Perturbations of the zero sets for functions belonging to each of these subsets are studied. It is shown that the boundedness of the real part of the perturbing sequence is a sufficient and, generally speaking, unimprovable condition for preservation the subset from which the function in question is taken. An application of these results to spectral synthesis problems for differentiation-invariant subspaces of the Schwartz class on an interval of the real line is considered.

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中文翻译：

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在零集的扰动下，保留根据沿实轴的增长限制定义的整个函数的类

摘要：定义了 Schwartz 代数的四个特殊子集（该代数由指数型和实轴上多项式增长的所有全函数组成）。研究了属于每个子集的函数的零集扰动。结果表明，扰动序列实部的有界性是一个充分且一般来说不可改进的条件，用于保存从中获取所讨论函数的子集。考虑将这些结果应用于实线区间上 Schwartz 类的微分不变子空间的谱综合问题。

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