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

The paper studies functions defined on continuous branching lines connected into a system. A notion of spectrum degeneracy for these functions is introduced. This degeneracy is based on the properties of the Fourier transforms for processes representing functions on the branches. It is shown that processes with this spectrum degeneracy are everywhere dense in the set of processes equivalent to functions on the branching lines. Some applications to extrapolation and sampling are considered.