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

TL;DR

This paper introduces spectrum degeneracy for functions on branching lines, demonstrating its density among related processes and exploring implications for extrapolation and sampling techniques.

Contribution

It presents a novel notion of spectrum degeneracy for functions on branching systems and analyzes its density and applications in extrapolation and sampling.

Findings

Spectrum degeneracy processes are dense in related process sets.

Spectrum degeneracy influences extrapolation and sampling methods.

The concept aids in understanding functions on complex branching structures.

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.