A theorem giving sufficient conditions for unique extrapolation and sampling of processes on oriented metric graphs, based on spectrum gaps that respect the graph topology, plus a density result with a proof gap for non-identity connections.
Spectrum degeneracy for functions on branching lines and impact on extrapolation and sampling
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abstract
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.
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cs.IT 1years
2019 1verdicts
REJECT 1representative citing papers
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Extrapolation and sampling for processes on spatial graphs
A theorem giving sufficient conditions for unique extrapolation and sampling of processes on oriented metric graphs, based on spectrum gaps that respect the graph topology, plus a density result with a proof gap for non-identity connections.