We obtain the criterion of solvability of homogeneous convolution equation in a half-strip. Proof is based on a new decomposition property of the weighted Hardy space. This result has relations to the spectral analysis-synthesis problem, cyclicity problem, information theory. All data generated or analysed during this study are included in this published article.

中文翻译：

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半带卷积方程的可解性判据

我们获得了半带状齐次卷积方程的可解性判据。证明基于加权Hardy空间的新分解特性。该结果与光谱分析-合成问题，循环性问题，信息论有关。在此研究过程中生成或分析的所有数据都包含在此发表的文章中。