TL;DR
This paper proves the Feichtinger Conjecture for certain Bessel sequences and shows that any Bessel sequence of unit vectors can be finitely partitioned into uniformly separated sequences, advancing understanding in frame theory.
Contribution
It establishes the Feichtinger Conjecture for a specific class of Bessel sequences and demonstrates a finite partitioning property for all Bessel sequences of unit vectors.
Findings
Proved the Feichtinger Conjecture for a class of Bessel sequences.
Showed that any Bessel sequence of unit vectors can be finitely partitioned into uniformly separated sequences.
Abstract
We prove the Feichtinger Conjecture for a class of Bessel sequences of unit norm vectors in a Hilbert space. Also, we prove that every Bessel sequence of unit vectors in a Hilbert space can be partitioned into finitely many uniformly separated sequences.
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 Analysis and Transform Methods · Holomorphic and Operator Theory · Approximation Theory and Sequence Spaces