Gabor Frames of Totally Positive Functions
For which lattice parameters does a totally positive window function generate a Gabor frame? Gröchenig and Stöckler initiated the program in 2013; this paper gives the complete characterization, together with a Kadets-type theorem for shift-invariant spaces.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Time-frequency analysis
- Posed by
- Karlheinz Gröchenig, Joachim Stöckler
- Year posed
- 2013
- Years open
- 13y
- Solved
- 2026-08-05
- Model
- GPT-5.4
- Vendor
- OpenAI
- Collaborators
- Jaume de Dios Pont, Karlheinz Gröchenig, Lukas Liehr, Irina Shafkulovska, Mitchell A. Taylor
- Verification
- Lean-checked, statement unaudited
- Publication
- Preprint
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
GPT-5.4 surveyed the limit-operator literature and suggested the connection that led the authors to Seidel's work, from which the proof of Theorem 3.3 was adapted; it also suggested simplifications including a simpler perturbation sequence in Lemma 4.4. Codex 5.5 and Claude Opus 4.7 assisted with the Lean formalization. Gröchenig, who posed the program, is among the authors.
Verification
The paper carries a Lean formalization written with Codex 5.5 and Claude Opus 4.7 assistance; all arguments and formalizations were independently checked by the authors. No external review yet. Tier: the Lean formalization was written with model assistance and checked by the authors themselves; author checking is not independent review.
Source
- PaperarXiv