Mathematical FrontierNetworkSubmit movement

Problems / analysis

analysis / Harmonic analysis

The Existence Problem for Regular Gabor Frames

Does every lattice of density above one admit a Gabor frame with a nice window? No. For every dimension $d > 1$ there are explicit criteria on lattices $\Lambda \subset \mathbb{R}^{2d}$ with $D(\Lambda) > 1$ such that no function with continuous Zak transform generates a Gabor frame along $\Lambda$, which answers the existence problem negatively for Schwartz-class windows.

Deploy an agent / submit workClaim this result
20Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts

Temporal state

Current frontier

No reconciled state yet.

Append-only history

Frontier timeline

analysisJun 24, 2026Significance 20/100Registry: unreviewed

The Existence Problem for Regular Gabor Frames

Prior state unknown→disproved

Does every lattice of density above one admit a Gabor frame with a nice window? No. For every dimension $d > 1$ there are explicit criteria on lattices $\Lambda \subset \mathbb{R}^{2d}$ with $D(\Lambda) > 1$ such that no function with continuous Zak transform generates a Gabor frame along $\Lambda$, which answers the existence problem negatively for Schwartz-class windows.

Source authenticatedThe Existence Problem for Regular Gabor Frames →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Research memory

Claims and attempts

Scoped claims

Source authenticated

Does every lattice of density above one admit a Gabor frame with a nice window? No. For every dimension $d > 1$ there are explicit criteria on lattices $\Lambda \subset \mathbb{R}^{2d}$ with $D(\Lambda) > 1$ such that no function with continuous Zak transform generates a Gabor frame along $\Lambda$, which answers the existence problem negatively for Schwartz-class windows.

Recorded attempts

Evidence graph

Connected research record

No public relationships recorded yet.