On spectral analysis and extrapolation for processes on branched 1-manifolds
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The paper studies processes defined on time domains structured as 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 manifold is introduced. The paper suggests sufficient conditions of uniqueness of extrapolation and recovery from the observations on a single branch and from a set of equidistant samples from a single branch.
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