# On recovery of sequences from subsequences: the case of non-periodic spectrum gaps

## TL;DR

This paper explores conditions under which sequences can be reconstructed from their periodic subsequences, introducing a new spectrum degeneracy concept and demonstrating dense recoverability within square-summable sequences.

## Contribution

It presents a novel approach to sequence recovery from periodic subsequences using a new spectrum degeneracy concept, expanding prior methods.

## Key findings

- Existence of a dense class of sequences recoverable from periodic subsequences
- Introduction of a new spectrum degeneracy concept
- Recovery applicable to all square-summable sequences

## Abstract

The paper investigates recoverability of sequences from their periodic subsequences and offers some modification of the approach suggested in papers arXiv:1605.00414 and arXiv:1803.02233. It is shown that there exists a class of sequences that is everywhere dense in the class of all square-summable sequences and such that its members can be recovered from their periodic subsequences. This recoverability is associated with certain spectrum degeneracy of a new kind.