The paper studies processes defined on time domains structured as oriented spatial graphs (or metric graphs, or oriented branched 1-manifolds). This setting can be used, for example, for forecasting models involving branching scenarios. For these processes, a notion of the spectrum degeneracy that takes into account the topology of the graph is introduced. The paper suggests sufficient conditions of uniqueness of extrapolation and recovery from the observations on a single branch. This also implies an analog of sampling theorem for branching processes, i.e., criterions of their recovery from a set of equidistant samples, as well as from a set of equidistant samples from a single branch.

翻译：纸质研究过程在时间域上界定,时间域结构为面向方向的空间图(或图示,或面向方向的分支图解,或分支图解),这一设置可以用于例如涉及分支设想情景的预测模型。对于这些过程,可以引入一个考虑到图示地形的频谱变异性概念。本文建议了从单个分支的观测中推断和回收的独特性的充分条件。这还意味着对分支过程的标本进行取样的相似性,即从一组等距样本中回收的标准,以及从一组单一分支的等距样本中回收的标准。