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Spectrum degeneracy and impact on extrapolation and sampling for functions on branching lines. (arXiv:1705.06181v1 [cs.IT])
来源于:arXiv
The paper studies functions defined on continuous branching lines connected
into a system. A notion of spectrum degeneracy for these systems of functions
is introduced. This degeneracy is based on the properties of the Fourier
transforms for processes representing functions on the branches that are deemed
to be extended onto the real axis. This spectrum degeneracy ensures some
opportunities for extrapolation and sampling. The topology of the system is
taken into account via a restriction that these processes coincides on certain
parts of real axis. It is shown that processes with this feature are everywhere
dense in the set of processes equivalent to functions on the branching lines.
Some applications to extrapolation and sampling are considered. 查看全文>>