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The paper studies functions defined on continuous branching lines connectedinto a system. A notion of spectrum degeneracy for these functions isintroduced. This degeneracy is based on the properties of the Fouriertransforms for processes representing functions on the branches. It is shownthat processes with this spectrum degeneracy are everywhere dense in the set ofprocesses equivalent to functions on the branching lines. Some applications toextrapolation and sampling are considered.

Spectrum degeneracy for functions on branching lines and impact on extrapolation and sampling