Proof of the HRT conjecture for (2,2) configurations
Ciprian Demeter, Alexandru Zaharescu
TL;DR
This paper proves that for any four points arranged in a (2,2) configuration, the associated time-frequency translates of any square-integrable function are linearly independent, confirming the HRT conjecture in this case.
Contribution
It establishes the HRT conjecture for all (2,2) point configurations, a previously unresolved case in time-frequency analysis.
Findings
No linear dependence among time-frequency translates for (2,2) configurations
Confirms the HRT conjecture in this specific case
Advances understanding of linear independence in time-frequency analysis
Abstract
We prove that for any 4 points in a (2-2) configuration, there is no linear dependence between the associated time-frequency translates of any function
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematical Analysis and Transform Methods · Mathematics and Applications