Spectral theory has become a central area of studies on commutative hypergroups. Spectral analysis and synthesis have been proved for different classes of hypergroups. In their paper (Fechner and Székelyhidi in Ann Univ Sci Budapest Sect Comput), the authors introduced and studied an infinite join of general finite hypergroups. Here we prove that under some general conditions spectral analysis and synthesis hold on that hypergroup.

中文翻译：

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关于有限超群的无限连接的谱综合的评注

谱理论已成为交换超群研究的中心领域。光谱分析和合成已被证明适用于不同类别的超群。在他们的论文中（Fechner 和 Székelyhidi in Ann Univ Sci Budapest Sect Comput），作者介绍并研究了一般有限超群的无限连接。在这里我们证明在某些一般条件下，谱分析和综合保持该超群。