2007.12647
Linear Dynamical Systems
Clifford Gilmore
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The uploaded paper (a survey) states the Bayart–Ruzsa theorem characterizing frequently hypercyclic unilateral weighted shifts on ℓ^p via the series ∑ 1/|w1⋯wn|^p < ∞, exactly matching the model’s statement. The model’s sufficiency proof follows the Bayart–Grivaux Frequent Hypercyclicity Criterion, and the necessity uses Bayart–Ruzsa’s difference-set method plus their series corollary—precisely the established approach. Assumptions (bounded, nonzero weights) are correctly stated. No substantive gaps beyond standard details delegated to the cited results.
Referee report (LaTeX)
\textbf{Recommendation:} no revision
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The survey text accurately states the Bayart–Ruzsa characterization for unilateral weighted shifts on ℓ\^p and situates it within the broader context. The model reproduces the standard proof strategy—sufficiency via the Frequent Hypercyclicity Criterion and necessity via difference-set techniques—faithfully and with correct hypotheses. As a survey, the paper need not include proofs; the key statement matches the literature, and the model’s proof outline aligns with the accepted arguments.